You can change that thinking by reminding yourself that everything they are accusing you of is not true about you, but it is true about them.
Take "rude", for example. You said it yourself yesterday. Your mum announced that she was going to come round later. You didn't want her to come round but you were too nice to say so, so you said you had other plans for the evening. A short while later you posted on this thread saying, "I can't believe it. Their car is on my drive. How rude."
How rude indeed.
You tried to set a boundary
You: don't come round tonight, I am doing something else.
Them: Surprise! Here we are!
That's not OK. There's no world in which that is OK.
Then all the phone calls. If a man you were seeing was calling you that often, several times in a row, then getting someone else to call or going round to your house when you didn't pick up, everyone would say that was a huge red flag and tell you to run for the hills. If a man you weren't in a relationship with did that and you reported it to the police, they would consider it harassment. So why is it OK for your mum and dad to do these things?
As for being a nasty person, the main reason why you're in this situation is because you're a nice person. You don't want to be a nasty person. That's why you're picking up the phone and saying, "Sorry, baby is napping right now", rather than, "Mum, Dad, I've got a baby to look after, and when I get a spare moment in my day I also need to feed myself, have the occasional shower, sit down for two minutes with a cup of tea, remember to breathe at some point, and WILL YOU JUST FUCKING FUCK OFF WITH THE CONSTANT CALLS AND UNSCHEDULED VISITS BECAUSE MY BABY AND I ARE NOT JUST OBJECTS FOR YOUR ENTERTAINMENT!"
I'd also tear an absolute strip off them for the comments about your baby's appearance and pinching her nose and all the rest of it. No, you're not being oversensitive. That is shitty behaviour and if they're still doing that when she's old enough to understand they're going to give her massive insecurities. If you don't want your six year old to be wanting a nose job your horrible mother needs to cut that right out.
Honestly, the best thing you and your husband and baby can do for your own sanity is move a couple of hours away.
This is not normal.