The other thing I wanted to say is that the nanny idea is an excellent one - if you are reliant on your MIL. It is great that your DD adores her gran, but I suspect that 50/50 joint care means that MIL will be doing a lot of childcare not that dad will be doing it.
Which brings me to my next point. Objectively speaking, what contact/residency arrangements do you think are in the best interests of DD? From what you say, you agree that 50/50 is the way to go. However, when he took DD away, it was temporary for a week, therefore my question is whether you are well enough in yourself to have her overnight at the end of the week? Because in the original plan, she would have been home, and any more was not agreed until she was out the house.
I have been told upthread I am minimising your illness. So if this is the case, please discard what I am saying. If it was me, I would be asking for my DD home, because that would immediately make me feel things were right with the world. It is where DD has grown up, her security. Great that she loves MIL and feels happy there, but a few days visit and something that stretches into weeks are two different things.
If you need reassurance, maybe ask one of your friends to come over while DD settles at night or to be on hand, but I am really not getting why a woman who does a job, looks after a house financially and domestically, and has done the majority of the childcare is suddenly not capable of looking after her child for a night in the holidays.
Forget potty training. I understand why you wanted it sorted in your time off. Forget perfect childhood, a bit of mess and disorganisation is okay. Just be there and play and have fun with your DD. As a poster upthread said, use your money for the support you need, not on your husband. He has left, he has given you permission to do this.
I am sorry, I will stop writing on your thread now. You are a capable woman and you will sort this out, you are doing the right thing with the advice you are seeking next week.