Struggling with partners guilty dad syndrome with his daughter

Firstly I am new to step parenting. I have been with my partner for over a year now and he has a 10 year old daughter. I met her just before she turned 9. I don’t have kids of my own but have a quite younger sister and have been brought up with young cousins so I’ve always been the helper when it came to helping with family kids. I have also been from a broken family and have experienced a step father and a step mother and was the left out child initially as both parents went on to have another child that became the princess so to speak. It was hard during my teenage years when I would be told off for the littlest of things by my step dad but his little princess could do not wrong. I’m only explaining this because I totally understand how it feels to be a stepchild and I promised myself if I was ever a step mum I would be nothing but loving to the step child.
Anyways I’m in my 30s now and was still unsure about if I wanted my own kids. I’ve met this guy and I said from the start I didn’t mind that he had a kid already (I was pleased she was older so to speak and not a toddler) we seemed to get on well straight away and she loved that she had another adult to give her attention. I did notice early on she absolutely loves attention but it didn’t bother me to start with. She is an only child and also has grandparents that absolutely obsess over her and she is their princess as well as to her dad.

All is fine and well but slowly over time small things start to develop that start to annoy me a bit.
Firstly-
She is an absolutely terrible eater. She only eats what she wants to eat which is basically either chicken nuggets or noodles for an actual meal. Then she fills up on sweets, biscuits, Lolly’s, bowls of sugary cereal. I brought this up early in a nice way about her being at a very important age for nutrients as she will be growing soon. OH agreed and decided we try get her to eat more stuff. For some reason this came down to me and I try to introduce more of what we were eating such as actual meat and vegetables. Tried a couple times and did not go well. She put no effort in trying but I felt it wasn’t my place so to speak. So I left it. It frustrated me but I felt was starting to cause tension between me and OH so left it. She pretty much went back to old habits and was left eating nuggets or ramen noodles.
However things took a turn when she ended up at the dentist and they said she needed 3 fillings at 9 years old. I mean I get this can be normal ish at this age but still isn’t great especially as this is her adult teeth now so they have decayed very fast. Tried to encourage healthier eating to OH again but he wouldn’t pursue it without me doing the dirty work which I didn’t want to do so left again. Few months go by and his daughter ends up needed another filling and a tooth taken out. When the tooth was removed the dentist apparently said it was really decayed. So at this stage I point out that she eats way too much sugar and doesn’t brush her teeth well I noticed. I said to him you allow her the worst kind of cereal which is just full or rubbish and allow her to eat rubbish. So after this talk she is with her dad for her time with us. Things have escalated where she doesn’t even eat her usual rubbish food saying she is not hungry but then minutes later raiding the cupboard for massive bowls of sugary cereal and biscuits. I was annoyed at this point and pointed it out to him. He continued to allow her to have it but said things would change after her tooth was getting taken out. After she went home I talked with him and I said I thing I know your problem. You’ve got this guilty dad syndrome where you’re scared to discipline her incase she doesn’t want to come stay at his. He agreed to certain extent and I do understand his issue but it’s allowing her to rule basically. I’ve noticed he babies her a lot which I’ve kindly tried to point out and say he’s not doing her any favours as she will be going to big school soon and if she’s like this she will get bullied.
To point out what I mean firstly-
-when I first got with him. he had all her toys all over the living room. A lot of them baby toys for literal toddlers. I threw them away with his permission as he admitted she didn’t play with them. Including Barbie dolls around the bath that were full of mould? (I felt like this was like a psychological thing where he didn’t want to accept she was getting older?)

• She doesn’t do anything while she’s here not even make her own breakfast. I get she doesn’t have to do chores since she’s here every week but just 3 days. But I did point out she’s fully capable of getting her snack cereal by herself but not breakfast cereal? He didn’t answer but said he likes to do it for her
• She can’t cut up her own food at 10 years old. Or pretends she can’t and still gets it done for her.
• My biggest thing is she constantly does not wash her hands after going to the toilet and we’re lucky if she flushes. This really annoys me and I’ve told her to do it a couple of times but why do i have to keep telling her. Her dad acts like he doesn’t notice this and I doubt this bothers him but it really really bothers me as I find it dirty and then she’s in the fridge and cupboards touching food. She’s coming from school that is a hub with germs. I find it lazy of her and could be easily resolved.
• Her bedroom is a bombsite. It was updated at Xmas but she’s had no consideration into the work that went into this and was trashed within a week. The problem is her grandparents molly coddle her and constantly buy her clothes and toys so her room is an explosion of clothes and toys. There is no discipline for her to look after anything of hers. She’s makes a mess and doesn’t tidy it.
• She expects me to do her hair for school. I did do it and would get up just for her even tho I work shift work and therefore most of my days off I have with her therefore waking up early on my days off even tho I’m not a morning person. I started to stop doing it tho when I started feeling the expectation for it and the demand to do her hair and then I started feeling like a maid rather than a family member. I started not waking up and then she would start waking me up to do her hair which really grated on me. I told my OH and put my foot down on it and from then on it kinda stopped happening. Apparently there were a few times where she had a huff and wanted to wake me up and got told no. Then a couple times she possibly lied saying I would do her hair and wake me up when I didn’t. This made me not want to do her hair even more. I got over it tho as I reminded myself she is a kid end of the day. However at 10 years old I’m sure she should be able to start doing her own hair. I think she can and I know she can do ponytails I think she just likes it being done for her. Also her dad can do it but she wants me to do it.
• She comes into our bedroom whenever she wants including when myself or OH are getting changed. I shut the door when I’m getting changed or shut it if we’re both getting changed but miraculously she suddenly needs one or us and wants to talk about summit so she’s knocking on the door two seconds later. Every time I’m getting ready she knocks on the door and it really annoys me. I tell her I’m getting ready and she just says oh. I now tell her I’ll be ready when I come out. This isn’t my house so I feel I have no private space and I’m someone that likes space sometimes and I’ve told my partner this. And I don’t mean disappear for hours. Even just a few minutes feels impossible. I’ve sacrificed my own home to suit my partner. I still have my own home which is now just sitting there not being used as it suites my partners needs better being at his as it’s closer to his daughter and her school. I tried to say at the beginning I want to be at mine sometimes even if it meant on my own but that still seems to not happen coz he takes it the wrong way like I don’t want to be in his house or his daughters company if I try do this so I give up so still paying for a house I don’t use now but I don’t want to sell it just yet.
• To help with his daughter’s teeth I bought a timer to help brush her teeth for the right time. She loves it initially but I noticed she’s stopped using it probably because she doesnt want to brush her teeth that long and being lazy. I told my partner who encouraged her once but then left it after. I just left it also coz at end of the day it’s not my teeth and she’s not my daughter. Just another episode of molly coddling her.
• She has a mobile phone which is a nightmare sometimes as she’s used it in the past to text lies to her mum and then her mum comes and gets her and this upsets my partner then he gets grief over things that aren’t true. She’s constantly on it or her iPad like sometimes I don’t see the point in her being here coz she’s just on devices. Unless she’s doing something fun which does happen every time she’s will us on a non school day, she’s always treated to days out at fun places. As soon as back him it’s back on devices. She’s even on them when she’s eating which I think is a massive no no and adds to why she doesn’t eat properly coz in her head the quicker she can finish the quicker she can go back to concentrating on silly YouTube videos and is not paying attention to what she’s eating. I’ve told this to my partner but he’s just brushed it off.
• I’ve just let it all be apart from one time where I felt crossed the line. which is where I was asleep one morning and SD was getting ready and dad was helping her, a normal morning. For some reason she decided she wanted my back pack for school. This bag pack had my important uni stuff in and important sensitive work documents as well as just a bunch of stuff. For some reason he let her have it without anyone asking me and I was non the wiser and woke up to the entire contents of the bag on the floor. I was really hurt and upset. He came home and didn’t understand why until I explained how rubbish it made me feel and I said I know your daughter will always come first and I understand that but you have put her before me over something very trivial and made her feel she can have anything she wants even if it’s something of mine which he had no right to do because it’s not his either. Once I explained it this way he understood and felt bad but didn’t really discipline is daughter and in the end she just thought she had to say sorry coz she made a mess on the floor. Which wasn’t the case but I just left it at that even tho I probably should have told her off.