Don't put pressure on yourself or your dd. If she has hypotonia and hypermobility, doing buttons is going to be very difficult for your dd for a long time. Even when she can do it, she will be very slow. You must make her teacher aware of this, so that she does not get told off or criticised for finding these things difficult - her self esteem is likely to be low enough as it is when she notices everyone else finding these tasks easy, without an adult pointing it out to her.
Hand (shoulder and arm) strengthening exercises will help - eg games where she has to pick things up with tweezers, playdough, writing on a blackboard, colouring in etc. The problem is, a lot of the activities that help tend to be avoided by low tone children, because they are more hard work than fun at first! Maybe you could find some really big buttons with easy, big holes, eg on an old woollen baby's cardy, that she could do easily and then work from there - or start off the process for your dd and let her finish off, so that she feels a sense of achievement, rather than having to do the whole lot herself in one go at first. And do buttons on things she isn't wearing before trying buttons on things she is wearing. Break the process down into manageable stages for her.
My ds1 has low tone and hypermobility and still has nowhere near the hand strength to do up buttons on trousers (too much pulling the material together at the same time as doing the button up), but can do small buttons on shirts, now (he's 6). He is slow at getting dressed and undressed in comparison to other children, though - it is much harder work for him. He also needed to be taught all the stages of getting dressed - seemed to have no instinct for it, himself! He taught himself to read, though, and do number sequences - he just has an instinct for things most people need to be taught, and needs to be taught what most people work out instinctively...
I think it rather stupid, tbh, that schools should put 4-year old children in school uniforms with lots of buttons and ties. The teachers deserve to have to spend lots of time helping the children, as punishment for creating a uniform that excludes the less physically able children from being able to exercise what little independence they are capable of. What's wrong with little airtex tops that you can get on and off without fiddling with the buttons?! Far better for a child's self-esteem...