How to deal with people like this?

My mom especially has a really irritating habit. If we are talking and she is stressed out, she will say something ridiculous that is very offensive.

For example, i talked to her about a return I had to make and I wanted to do an exchange instead. It went from her saying no to me saying ok and her making comments about me "needing to control my spending habits, wanting to be like my friends who shop a lot, and not being able to be told no and that she needs to keep quiet around me and comply because if she doesn't I'll blow up at her",

Obviously she made me angry so I got progressively more angry. I tried to be logical in the beginning but she pushed my buttons and I showed my anger outwardly. Then my mom picked on what an angry person I am.

That's a tame example but she does that a lot. Get stressed, say provoking things, get a reaction, then pick on my reaction.

My sister does a very similar thing.

How to deal with situations like this? So far I try to not give a reaction and I hold it but eventually they push me so much I react, sometimes with strong anxiety symptoms like hyperventilating.

I try walking away or leaving but they follow. I don't like being silent about it and just not giving a reaction. I would like to be more proactive if possible.

I have tried talking to them about this and they don't comprehend. My mom says I talk too much and just want to pick a fight and she picks on what I did when I was angry. Same with my sister
How to deal with people like this?
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