I've read the thread.
I feel sorry for MIL. She's clearly giving up her time trying to help, please remember that.
My DCs are grown now and from what I read things are very, very different in child rearing now. It's hard to break your habits and it's also hard not to think that because you did it and coped a certain way, that other people should find it the same.
To give it some perspective my DH had no parental leave at all and when DD2 was 10 days old his company sent him abroad, with the two weeks planned turning into a month. I had a little one, a newborn, pets and dodgy builders from hell all to cope with at the same time.
I coped because I had to, there was no outside help.
Sometimes that actually works because there's absolutely no conflict of interest and you just have to find a way that works as best you can.
It's a shame that MIL's presence isn't taking all the stress out of the situation, in a perfect world she would just do exactly what you ask and do it without comment - but we're not all perfect and it sounds as though she's trying by taking DD to nursery and getting your meals started.
I feel sorry for your DD OP, who has always been your focus and now sees a new intruder taking her place. She's only tiny herself, please don't feel resentful towards her, she isn't behaving this way to challenge you or make your life difficult. It's very early days in a huge period of readjustment for her.
I feel sympathy with the new baby who's trying to find its place in the family and way in the world.
And I do feel sorry for you OP, you sound very stressed and challenged - everyone sounds stressed, which won't be helping.
I think you either need to go it alone and do as you do without criticism, or you need to have a bit of a heart to heart with MIL and explain that this is how you want to do things and could she do X, Y or Z to help you out.
Maybe you could start getting DD ready for bed earlier and let her have story time snuggled up to you while you feed your baby? Change her routine to suit the new household but still let her feel she has your time and isn't being relegated to second place.
Most of all, remember we all have shitty days and we all do have feelings we're not proud of in the heat of a moment, let it go now and just concentrate on doing the best you can at the time and enjoying your girls.