I moved from Glasgow to London last year to take my dream job, leaving my childrens father in Glasgow with his gf and new child. he is always welcome in our house, as the kids father (circumstances dictate that they cannot stay with him, the house is too small and belongs to his gf)
we split up over ten years ago when our youngest was 9 months old. (children are now 16, 13 & 12) he had a relationship with another woman and left us. I stayed in Glasgow miserable for ten years, so that he could see his children. For a couple of years, I dropped them off & picked them up (round trip 50+ miles) so that he could spend alternate weekends with them - he had lost his driving licence. I haven't received maintenance in so long that I can't actually remember (& I appreciate that these are two seperate and distinct matters) I feel that I have been as accomodating and amicable as possible...so when my dream job came up - I took it. we moved 450 miles away. .
we're happy. kids are settled, their father is encouraged to come and see us as often as possible. there were bad, dark periods when we lived in Glasgow where he ignored them for months on end/
In my circumstances ( & this may not apply to OP) yes, I made a commitment to my children to put them first when i had them and yes - I made a commitment to my ex when I chose to have children with him.... but he didn't hold true to that commitment. He broke the promise.
It is individual circumstances. It won't work for everyone, people have varying personal circumstances , as exampled by my personal experience above - it is impossible to know everything about the OP from her post. It might work and it might not - it is a calculated risk and i think it is very dependant on how old your children are and their personalities and relationship with their dad.
it's difficult to stay and difficult to go :) No matter what you do as a mother, sometimes, it just isn't the right thing according to someone else.