It helps to get things off your chest and talk about them, no need to apologise.
Yeah, you're right there. Be you, and they can either accept that, or not accept it, but if they don't, its their problem and their loss.
And they should see that just because you're not living with them doesn't mean you can't still have a good connection and see each other if you want to. Most people move out from home at some point. So its them that would need to change their outlook, not you.
I can imagine that comment from your mum must have hurt your feelings. You don't deserve that for going to visit her. And sorry about the animals, I can understand that must be very sad for you. Is she not prepared to discuss it and come to another arrangement? If not I would just try my best to accept it and not dwell on it too much in my head, as that will make you feel worse. Although I know that must be very hard.