Wheres your father?
OP, your dh could arrange something, to help you out.
If your mental health deteriorates, you could fund him having to take extended leave to care for you and the baby.
The issue, is that wanting regular free childcare, isnt something they cant commit to. My mum did this for dbro and his wife, she also worked and it just exhausted her. As well as caring for her father. I say caring because he didnt need that much. But did need someone to go in each day, check his medications, check he was ok. He had early stages of dementia. He could be fine for weeks, then go off the deepend. Day to day, she didnt do a lot for him. But its stressful.
And have you though about how you will feel if your baby is ok, for your mum and mil? At least with a professional, you wont feel as bad. I have seen it on here and real life. People desperate for a break and the they get it but get upset cause the child is ok with someone else.
Mum just felt that she didnt have anything else to give. Even just doing it one afternoon a week.
Before you baby came along how much did you and your dh do to alieveate the stress on your mother and mil looking after relatives?
I have to say though, unless you ask them outright, then you cant really moan.