AITAH for telling my mother in law that she isn’t welcome in my house

I'm 29 male. My wife(28F) and I have been together for 8 years, married for 3 years. I've always got on with well with most of my wife's family, though her mum is often busy and don't see her much but she's never been weird or rude to me.

My wife's parents have been staying at our house when there house is being renovated. They've been here for 3 weeks (renovations estimated to be around a month). My MIL starting acting weird about a week in. First thing was my wife and I were going out and I said I'm going to go and have a quick shower, my mother in law said "we don't need to know that", I was literally talking to my wife basically saying I'm gonna go and get ready to go out.

Little digs like that.

Then she says we have way too many pets (we have 5 dogs and 3 cats) and should get rid of them. They're all well behaved and trained, aren't rude around food, we keep the house clean and smelling nice. I've always had 4+ dogs in my life, this many animals isn't a lot of me and my wife also loves having this may too. I kind of brushed this of as I know this many animals isn't for everyone.

Then I saw on our outdoor cctv that my MIL purposely left our back gate open, off the latch (our dogs have access to this part of the garden). I confronted her about it and said that our dogs could have gotten killed (the dogs know not to go out of the gate without permission but they CAN make mistakes) and she apologised, rolled her eyes and said this "little" slip up wouldn't be stressful if we didn't have so many dogs or none at all.

Then the one morning I had just woken up, went downstairs to get coffee for myself and my wife and my MIL says the most random and weird thing, "do not have sex with my daughter while I'm under the same roof as you". My wife and I didn't have sex that night so it's not like there's any chance we were accidentally too loud (which wouldn't happen anyways because we'd make sure to keep it down anyway. I told her to mind her fucking business. She then went on to say that I'm an asshole and I'm the worst thing to happen to her daughter and that she hopes I never impregnate my wife because it would be a nightmare if I had to be part of their family indefinitely.

I told my wife about this and she was also pissed.

AITAH?