Feeling rejected by DSD. How can I make this better?

[Carrottes]

I'll start with the back story...

DH is German and was with his childhood sweetheart from a very young age. He got a contract working in England in his early 20s and moved over with his GF. They had a baby but split up after a year or so as gf was finding it isolating and hard being away from her family. She moved back to Germany with their daughter and they carried on a long distance relationship for a couple of years but split properly when daughter was around 4yo (initiated by her as she had met someone new, although he is no longer in the picture).
DH stayed in England and travelled to Germany as often as possible to see Dd.

Fast forward one year and we met. We were together for a while before we introduced children etc (I have a son two years older than his DD). We got married 3 years ago and now live together.

At first it was okay with DSD as she seemed to like me and my son but as she has got older it's become more difficult.

She finds it hard seeing her dad living with us - which i totally understand but I was hoping as she got older it would be getting better rather than worse. We have her every school holiday and whenever dh gets two days off in a row he will fly over, rent an apartment and do school runs/normal life as much as he can. He works on weekends so can't see her then but I really must stress he tries his hardest to see her as often as he can given they live hundreds of miles apart. They FaceTime most days.

His line of work is quite specialised and there are no opportunities for him in Germany. This is why he originally moved here with his ex.

So to get to the point of the matter there have been a couple of things that have happened recently that have upset me and I just don't know how to deal with them.
Firstly... She has said that she wants another sibling but not from me with her dad, but from her mum and dad 😑.
DH and I have talked about having a baby together and on one hand I would love to but on the other I can see it causing a whole host of issues for her and I don't want that (but I'd really really like a baby...)

Secondly he booked some time off and went over for a long weekend for Father's Day to spend it with DSD and Ive just seen the card that she wrote for him.
Inside it said "I really love you. My heart is full with love for you and mum. Although I don't appreciate having Carrottes and her son around" and it went on.
DH doesn't know I've seen it yet.

I just feel so down about it. I don't know what to do. When she's here we get on well but now I think she must be faking it ??
I primarily feel sad for her that she misses her dad so much but I also feel upset because I feel like there's nothing I can do to make her like me more?? Apart from leaving DH of course, pretty sure she would love me then.

When she's over I make sure her and her dad get plenty of time on their own. It's not like I crowd them and try to muscle in on their daddy daughter time.

Ugh I'm feeling a real conflict of emotions. Sad for her but also a bit annoyed.

Wow sorry for the length of this I needed to vent. I'm not sure what I want out of it to be honest 🙈

Thanks @Anuta77 that was a really helpful post. I think your DH is right in that my DH needs to talk to her about it properly. But because he doesn't see her as much as he or she would like I'm sure he's apprehensive about potentially turning their time together into upset for her.
I get it, I really do try to understand.

I'm taking my step back and going to wait to see if the tide will turn.

I know it’s not an easy regular set pattern to when your DH sees his DD but if he’s having her every school holiday then it’s actual more in terms of the amount of time a lot of kids see their dads (comparing it to EOW access which is pretty standard).
I find it a bit odd she’s talking about your DH and her mum getting back together, you’re married and she won’t remember them being a family together. Also at 13 she knows exactly what she’s saying, unless she’s particularly young or immature for her age? I have a 14yr old SD and she would no better than to vocalise feelings like that, it seems more like something a 6-7 year old would say.

I don’t think it’s personal so keep being kind and your usual self. Hopefully she’ll come around again and you’ll end up with at least a nice friendship when she’s older.

I was also going to say that I think that so much one on one time is too much & that your mil is right but I reckoned I'd get flayed! Then @Anuta77 said it in her very insightful post. Due to geography & logistics your dsd is being treated as very special (which she is of course, but so are all kids to their parents) & seems to have (& now expect) both her mum & dad's undivided attention. But that's not how real life works; in all relationships as we get older we have to share people's time & attention be that in a romantic, platonic, familial or work related way.
I would also say there is a difference between her dm saying she doesn't need to meet you as she trusts you're doing a good job when with her daughter, & her dm saying she doesn't want to meet you.

I have plenty of contact with my kid's dm but my dp's ex refuses to meet me (bar yelling at dp the few times I had to be in the car with him when collecting the kids) which I think is just denial. My exh's dw & I are not 'friends' but we're friendly as my kids live with her when they're at their dads.

FanjoFizz (loving the name!) she is quite young for her age imo. Although I don't have experience with a daughter I can only compare to my niece and my DS but some of her behaviour is still quite young. In a sweet way though! For example she writes him letters with poems and hearts drawn all over. She really is a daddy's girl so it must be exceptionally hard for her.

(Note - this May well be normal 13yo behaviour but I can only compare to my niece who would rather eat her own toenails than do this haha!)

Do you get on with her mum? Sorry if I missed you saying this already.

My DD is 9 and would cringe at the thought of doing that. It’s sweet but it’s very telling of her relationship with her dad, like she’s used to being babied and maybe a bit of a princess. I may be way of the mark here, but it sounds a bit weird for a teenage girl.
I’d be wary of signs of mini wife syndrome creeping in over the next couple of years.
She does need time with her dad but it’s unhealthy if she isn’t expected to blend in with dad’s wife as a part of her family too. Too often problems can arise due to SCs being treated like they are fragile and may snap if they’re not given undivided attention or top of the priority list.
They won’t, they’ll be fine as long as they’re given love and shown kindness.

@Carrottes - just seen your last post & ime it's not normal 13 yo girl behaviour. My dd is her dad's only girl (she has 4 brothers) & would have done stuff like that up until about 2, 21/2 years ago. She's still very affectionate but in a much more grown up way & has now moved on to writing both her dad, & me, funny cards as opposed to gushing ones.
As a pp said I'd be wary of mini wife syndrome - it really is a thing.
12/13 is the age when a child's peer group becomes more interesting than mum or dad so that level of intensity being directed at a parent is a bit off. I know your dsd doesn't get to see her dad the way other kids do but it's been that way for years so to an extent she should be used to it.