Don’t write a long text or letter. It won’t work. Been there, got the t-shirt. They’ll ignore it but hold a grudge, get more upset or they’ll pick it to pieces. I imagine your dad will do the 1st, your mum, the 2nd and not sure if they’ll do the 3rd to your face but it sounds likely they will between themselves.
Right now, you’re incredibly reactive and hyper vigilant of everything your parents do and say, especially your mum. Up until now, you’ve managed this by doing exactly what they say. I get it. This is what I did with my brother and wife before going nc. Anything else doesn’t work. You’re huffed at and criticised, even if they move the goal posts and plans because you cannot immediately fit in. Your parents also sound like brother and sil in that they talk about you as though you’re subhuman and by extension your dd, are competitive and so forth. None of is normal at all, walking on eggshells. I get it. I lived it.
Well done for managing to have a calm talk with your mum. I struggled with this one hugely. I think right now, you just need to ride this out until they leave. You’ve said what needed to be said. Pretend you haven’t noticed the frostiness. In fact, you and your dad are both having a similar reaction. Both pissed off for different reasons. Neither wants to talk. So he feels like you do, whether he’s justified or not is a different story.
What I’d do when they have gone is get some therapy if there’s any spare money as that will help bolster you. If not, keep talking on here anyway. Then look up narcissism and triangulation, previously mentioned. Also, look into boundaries and parentification. There are two types of parentification. One, where you’re expected to do physical stuff for your parents and act as their parents or the parent to siblings even though you’re a child. The other is emotional, where you are trained to look after your parents emotional needs. I was parentified and like you, hyper vigilant as a result. Two things cured me to a large extent. Firstly, therapy, secondly illness. I just can’t do stuff anymore and am disabled.
Not long now and you’ll have your house back. And to quote Caroline Bingley in Pride and Prejudice, it will be ‘so refreshing to have one’s house back to one self again’ or something along those lines.