You are NOT a bad person (VERY MUCH the opposite). You are NOT being punished by God for anything (God is not a "punisher" at all, you are just in a bad situation). You have done nothing to DESERVE your bad situation, no one would deserve mistreatment by their family or by their fellow human being at all).
I'm a 53 year old male who has grown up in a dysfunctional family and suffered 51 yrs. of suicidal Depression
because of it. My Depression
ended when I became the last living member of my family, so believe when I tell you that you are reacting to your situation as any rational and sane person would.
I also was the most gentle and kind person in my family, and they chose to see this as a weakness that they could abuse and exploit. There is nothing wrong with you, you have a very good heart full of love.
Because you have a very good heart, you also have a very keen mind (insightful) and can see very clearly that the "conversation" was really not a true conversation. A true "conversation" will be a DIALOGUE (2 people speaking to each other), not a MONOLOGUE (1 person speaking, as in a "SPEECH").
Notice these things about yourself, you have an insightful mind and a good warm heart. You know that love is not just another EMOTION, you know love as a SENTIMENT (the only REAL sentiment, "HATE" is egotistical RESENTMENT, it is not a REAL sentiment because it's made up of EGO and RESENTMENT). So, there is nothing WRONG with you, there is something wrong with the WORLD, and something very RIGHT with you.
You have no reason to feel guilty or ashamed about anything you have done (you can feel UPSET "about" what has happened, but you are not RESPONSIBLE for CAUSING it). You did what you could about the cat (what were you supposed to do?...YOU'RE JUST THE CHILD in the household). You did what you could (and all humanity thanks you).
You don't realize this, but it was very insightful (of keen mind) for you to be able to notice AND EXPRESS this so well as you did...
"bitterness, negativity and anger"
It is also insightful to notice that your mother feels guilty...YES, that's right she does. That's why she can't acknowledge how justified you are in your anger,...because then she would have to admit her guilt to herself (not just to you). What she's doing to you by not sticking up for you is wrong, but she is also in the prison of her own mind (someday, when and if you feel up to it, remember that you have the option of rescuing her like you wanted to do with the cat).
You have not been RUINED (you have been betrayed, but not ruined), but are you going to LET this situation ruin a human being (yourself) that has such a truly GOOD (rare) heart and mind? (I'm not saying this to patronize you, I'm 53 yrs. old and know that someone who reaches out for help by coming to this forum as you did and writes/feels as you do is TRULY a VERY good heart and mind,...RARE).
Any sane person would feel abandoned in your situation, believe me, your mother feels that way too.
"I feel abandoned"
Not to disregard your pain, but your mother senses being "abandoned" by you not considering her prison sentence (or do you only care about your abondonment?).
I value FAMILY very highly (by contrast). If you had a "heart to heart" talk with your mother (not soon, but when you feel better), your mother might admit her guilt, apologize, and you would have the option of forgiving her (as an expression of your heart, that might do you some good, it would certainly help rebuild the family).
Think it over,..the choice is yours, you can do nothing to change the past, but the future is wide open, nurture your heart, reclaim and covet your family.
Repair a bad situation (in a family, self-redemption is MUTUAL redemption).