...they do all these things independently and without fuss when he isn't here (and at nursery and school)
To those asking how the girls are going to manage at school - they are apparently doing fine.
Busybecca
Your question to me is very general.
If you mean should you tell the girls off for wanting their dad to assist them every step of the way to use the loo, the answer is no. There is nothing wrong about this element of what is going on. If you have anxiety about it, please dismiss it.
If you mean should you tell the girls off for rudeness, screaming, tantrumming, and demands at high decibel (for example while he is in the shower) then the answer is yes.
Your girls are fine when it comes to taking care of themselves - they are well able to perform self-care tasks when they are with you and away from home.
Relax.
As MotherHen says, none of the babying matters. Children vacillate between independence and being babies. Normal healthy parents vacillate between fostering independence and babying. It all evens out in the long run and even in the short run.
But the rudeness and the bossyness and tantrums matter and you need to stop that. It is up to your H to 'baby' the girls if he wants to after that. It will not have a bad effect on them, as you have already seen in their school performance.
As an example of focusing on the elements of their behaviour that are unacceptable - you recount an incident where DD sneezed and needed a tissue.
Instead of telling DD to get a tissue for herself since she was well able to, and saying that dad couldn't hear her because he was in the shower, you should have told her it was rude and unreasonable for her to bother her dad in the shower and that it is never ok to scream and yell at someone the way she was carrying on. You could have asked her what would happen if she behaved like that in school if you really wanted to hammer your point home. When you told her that dad couldn't hear her she may have decided extra decibels would help.
You have to stop this bad behaviour. You completely overlooked it and focused only on what DD wanted and the physical obstacles to getting it, whereas the point of your interaction with her should have been that it is not ok to bother someone while they are in the shower. This is how you teach boundaries.
'Dad can't hear you' is not the way to get her to understand that it is not ok to bother dad while he is in the shower. That only invites a higher decibel level. You have to spell it out to her that bothering someone in the shower is not acceptable and screaming when someone doesn't respond is also unacceptable.
(Channeling Supernanny here with the word 'unacceptable', sorry.)
As an example of where you need to relax, you remarked that you have told DD that if she can't get onto the trampoline by herself then she can't use it.
I'm left to deal with the tears if she does it when he's not here and I tell her she can't use the trampoline if she claims to be unable to get up and down by herself.
You should take MotherHen's advice and do some babying.
All the effort that you have put into teaching your girls self-care will go to waste if you continue to imply to your girls in incidents like that that once they can do a thing there is no valid reason to expect help with it from you. This behaviour on your part will kill any joy they may feel about their abilities. You must always seek to preserve the relationship when you foster independence, and with children of 3 and 4 that involves assuring them that you are still mummy as they have known you for the course of their short lives.
You should focus on maintaining their joy in accomplishing tasks by themselves, which will help them to try to be more responsible. They need to feel at the same time that you are a soft place where they can land - to penalise a 4 yo for wanting some babying (help onto or off the trampoline) is to ignore completely her emotional needs. Worse, you make her feel bad for having that emotional need.
Again, do not get bogged down in the details - the fact that she is physically able to get onto and off the trampoline is immaterial here.
What is important in all of this is what the girls are saying about their emotional needs. You are failing to recognise this.
Somehow or other, you and DH are so separate in their eyes that what you have taught them about how to treat you is not recognised by them as a general principle to be applied to everyone. When it comes to behaviour towards your husband at home, they are clearly in need of some solid leadership. They behave for you because you have succeeded in setting good boundaries around yourself. It is time for you to step up and demonstrate to them that you and DH are two halves of the same coin and what hurts one hurts the other. This needs to be made very clear and you should not let any opportunity slip past to comment on bad behaviour towards your husband. It doesn't matter what they want or whether they are or are not capable of doing a task for themselves. That issue is beside the point and not important in the long run. Do not get bogged down in the details here. The big picture is bad verbal behaviour towards dad.
Your posts are filled with exasperation and frustration with this man. I cannot believe some of your attitude towards him is not reflected at all in your home.
You and DH need to do couple things together, if you don't already, that show that you are a loving couple. Do you go out on the odd date together? Do you do small things together at home to demonstrate that you love each other? Say 'thank you' to each other with a smile? Make tea or coffee for each other? Pour a drink? Make it clear to the girls across the board in all interactions possible that your husband is important to you. What special thing did you and the girls do for him on Father's Day?
Your girls need - first, last and always - reassurance that you and their dad are happy together and focused on each other.
In fighting over how DH treats the girls/how you treat the girls you have given them a role that is terrifying them - it is the role of 'people who can get between mummy and daddy and cause them to fall out'.
You need to remove that burden from their shoulders.
You need to restore their sense of security.
You have to show leadership here. You have to compromise and do some babying. You have to do your utmost to stop the unacceptable behaviour, the demanding, shouting whinging, and tantrums. Do not sweat the detail of whether they can do X,Y or Z for themselves. The specific thing that they want does not matter. What matters is how they conduct themselves.
Their future lives do not hang on dad doing things for them that they can do for themselves or you refusing to do things for them that they can do for themselves. Their misery as they play the role of people who can treat an adult whom they love (and they do love their dad) like shit while the other adult whom they also love lets them get away with it will harm them greatly.