He sounds like a twat. Of course charge him as normal- just keep her out of the argument, as I'm sure you'll do anyway. Your mum, of course, loves her, but must have lots of old lady type hospital visits to sick friends etc to do if he asks.
I htink you should tell your mum what he is oding, and maybe between the two of you suggest he makes proper arrangements and sticks to them. If you let him keep getting away with thi, it will never stop. Its not being unreasonbale, but for some people, you give and inch and they will take a mile-he is clearly one of them! I would tell him you need regular hours now, you need the financial stability (as is only right) not payg.
Of course you are not being U. He is blatantly exploiting your good will and your mum's. Quite apart from your own issues, the thing that stuck out for me from your post is this. He is going on holiday without his 12 year old daughter in half term. What on earth is he doing that for? Reality's uncle, for example, is a twat.
I know she's only 55, but it helps to start cultivating old lady type things from a relatively young age (I have started ) with which to baffle and mystify people who would make demands on your time. You have to say things like "I'm far too busy for that since I retired- there aren't enough hours in the day!", while leaving everyone quite unsure as to what it actually is you are doing. You must always have "jobs to be getting on with"...I'm teaching you to suck eggs here though: you are an expert at artful procrastination, obviously, as you are on mumsnet as much as I am . it takes skill though to convey the impression to loved ones that it is importantwork though- that's what I'm aiming for...
It must take all your restraint not to tell him to F off next time he wants a "favour", but you're more concerned for his daughter than he is and you don't do that because he can't be trusted to arrange decent care for her otherwise. I'm not really sure how you sort him because he knows that your niece's wellbeing is your Achilles' heel.
Have you or your mum, or anyone else in the family ever confronted him with what a mean, using, useless twat he is ?
He sounds like a prize nob. He taking advantage of your kind heart and your attachment to your cousin. He knows you won't do anything to upset her.
Definitely think it's got to be down to your mum to tell him that he needs to stick the original arrangement. He just seeing what i can get away with - did her not think that she would not like to go away with him???
Poor, poor kid Luckily she has people like you to care for her.