I'm sorry to hear about that. I haven't told my mother explicitly about my AB side, she found my baby toy stash when I was a teen though and responded poorly, so I know she would likely be against it as well. We'd like to think that our parents can accept us for who we are, but at the end of the day, they're people too with their own concerns and hang-ups. That being said, they might not understand, but they'll always love you.
First off, I'd like to tell you to hang in there. You're young and one day, when you are out on your own, the opinion your parents have regarding this won't mean much of anything.
Secondly, trying to quit being an AB or a DL is fighting a losing battle. Even if you can set the desires aside for a while, as you are living under your parent's roof, they'll still come back eventually. I know for a fact that my being an AB will never go away, I've even had lulls in my baby and regression time where I won't engage for weeks, sometimes even months and at the end of the day, the desires still come back and I wind up diapered and in baby mode when I have the down time. Trying to repress, conceal and remove this side of you can be toxic as well and could lead to depression.
When everyone else fails to accept you, just be sure to accept yourself, that's all that counts. Self-acceptance is the foundation of leading a positive and fulfilling life as an AB or a DL.
I'd say for the time being, maybe you could try to keep your DL side on the down-low until you get a place of your own.
Don't worry about the psychologist thing too much either. Many psychologists are quite progressive and understand that fetishes and alternative lifestyles are harmless and something that can't really be changed. It does worry me however, that your mother is the one setting up this appointment. If she is not accepting, she might be actively searching for a psychologist that isn't kink friendly or aware. Sometimes, talking to a psychologist can bring a new perspective on things and aid in self-acceptance, I have heard of many people having positive encounters with a psychologist that understands to some degree the ins and outs and the immutability of fetishes and alternative interests. Could you maybe try to meet your mother halfway, maybe agree to see a psychologist, but see if she'll let you choose who you end up having a session with? If she's not a total tyrant, she'll give you some say in the matter. Maybe you could find a progressive, kink friendly psychologist that you can set up an appointment with? Furthermore, where I'm from, once you are over 18 you're considered an adult, I know if I was back at the age of 21 and I was being pressured into having a session with a therapist or psychologist, it would have to be with someone I felt comfortable with and I certainly would be the one scheduling and setting things up, not my parents.
In any event, I hope things work out for you. Try not to get down in the dumps, just know that as soon as you have a place of your own everything will sort itself out. Until then, grin and bear it and try not to let it get to you.