Welcome to bb forums, I hope to provide some small advice, but I've never been a single mum!
I'm a childless male with a long term wife, though I have done plenty of customer services work over the decades.
Fortunately all that aint so relevant to my way forward I'm gonna suggest... which is,
Take a fine tooth comb to your employment contract, or whatever written stuff the business has given you. And find in that contract what you need to express your families need. If you can't find it, and after talking with someone at work you still can't meet your families needs, then I advise quitting. Family comes first in my opinion.
If the contract says you have to put something in writing or in advance to have a request for different hours, then do it.
If the contract says talk with the boss and negotiate, do that.
If you find yourself after writing your needs and speaking about your needs to the business, and remain unable to meet your families needs. Then make it a complaint to the appropriate person at the business or the businesses owner or _____. Human resources. Work place counsellor. Work place occ health safety. Anybody you can think of who might be able to from within the business help you keep the job, but have those slight changes to your hours.
good luck, hope that helps.