' it’s literally the finances I feel like I’m banging my head against a brick wall with. '
Because they don't work for you and your family. That is the bottom line.
'In my head I was in the stance of ‘I can’t ask him for more’ but reading these I think I will as like you’ve all said.'
You should have to, but that's exactly what will happen if you move in with him, and he start pressuring you to do things that make it easier for him.
Never, ever, ever become financially dependent on someone else in an unmarried relationship, especially when you have two children relying on you for their welfare.
None of this adds up here, for you, you, and your children, stand to lose a lot.
He's no keeper if he keeps pressuring you to make moves that will disadvantage you and your children so much financially.
He wants to move closer, he's an adult, let him do it.
And tell him, 'Moving in together makes my family too vulnerable financially, so it won't be happening right now.'