Yes I do sort of agree, obviously it totally depends on your role, but WFH and looking after a little one I've found to be basically impossible on the rare occasion I've tried it, I've always ended up taking annual leave/sick leave to look after my daughter if it's one of my work days and she's not been able to go to childcare for whatever reason.I am in no way saying they are right, but I do kind of see where they are coming from with saying you can't work from home with a baby. I am assuming that they are thinking that you concentration will be split ect. If you're not sure how you're going to afford being home, is there any way you could start looking for online/WFH roles now? Even if the pay isn't fantastic, you might be able to find something to top up your income.
That said, you'd hope they would be more flexible to do adjusted hours or something like you've said, that sounds like a really good idea.
I would put in a formal flexible working request requesting that change in working hours/pattern and see if they have a good reason for rejecting it.