OP, you say your parents are very wealthy and that you are in a crunch point, where things are likely to be as tight as they will be for some years. Soon there will be financial relief, both in terms of outgoings (lesser childcare fees) and incomings (you and your husband both making more money).
I'm going to say something slightly unpopular, that I say only because you mentioned your parents' situation: I think you should talk to your parents. Would, say, £5,000 be very likely to make a difference to them? If they're very wealthy, I imagine not. It would make the world of difference to you.
There is no shame in family helping family. Think of it this way: if you were very wealthy, and your child, whom you love so much, was struggling, wouldn't you want to help her?
I say this as a child of wealthy parents, from a wealthy family. When I was starting out, my father gave me £300/month to help with rent, which was the difference between living in a decent neighborhood and having a couple nights with friends a month versus struggling. It made me squirm to accept it and it made me feel guilty. Until he said that to force him to watch me struggle and not enjoy life while he had the means to help (a means that was in no way a stretch for him, and that he would barely notice) wasn't being independent or noble, it was a bit cruel. I was working hard in a good job, just in an introductory role--I wasn't a layabout, nor was I greedy or feckless. That £300 meant the world to me.
It also helped to think of this: he said that he'd rather give me money now than leave it to me when he died, that people need more help in their 20s/30s than their 60s, and that he wanted me to enjoy life while I could.
I think we're taught to be self-sufficient and proud. That is good. But we are also families who love each other and who work towards the same goal: each other's happiness. I don't know your parents circumstances, and I don't know your relationship with them. But I realised I had been seeing things from my own perspective (a child determined to be independent from her parents) and not from his own (a father who actually delighted in helping his children and watching them be happy).