@SimonJT I am sure you are trying to help but....
your 'solution' appears to be that the OP moves out and leaves her children with this man. Why would she do that?
All children are entitled to 15 hrs a week free childcare over a certain age.
Also, she didn't say he was not changing the nappy- this appears to be posters' 'Chinese whispers'- she said the nappy was clean but he had not dressed the child.
In the longer term OP, you need to think about getting training and qualifications so you can move beyond a minimum wage role, and earn decent money to support you kids and yourself.
Look into creches that are provided by colleges of FE, look into free childcare.
You need to tell your DH you want a divorce. But before then get your ducks in a row and see a solicitor. Some will allow you a 30 min free chat (not all.)
You and your DH need to sit down as adults and discuss the care of your children and how it will work without going to court, which is a nightmare, and work in the best interests of your DCs.