1st of all, Congratulations! It sounds like you have so much happiness to look forward to! I am so happy you have a life that you are proud of and feel happy about.
As to your mom, ...Well, your mom is finally having to face that you are a grown up. That you have a life separate from her and that your life (and more importantly to her: Her life) is about to Really change when you get married.

She is having a hard time letting go of you, she is losing/has lost control. Of You. It sounds like you are her world, and now she is afraid of being left behind. That is why she is attaching emotion to things, pets. She is grasping for something to push your buttons with.

I think, if I were you, I would move out, before you get married. You need some separation time to establish yourself as an adult in her mind. And for yourself. Don't take much in the way of belongings, except those things that are truly your personal belongings, & gifts from her, etc. Her home should be left intact.

Besides, you and your fiance will eventually want to create a home together, choose things together that can be taken to your new home after you marry. Her things are hers.

It sounds like she is afraid you don't/won't need her anymore. But by being level, logical and non emotional, her outbursts should make your realize they are more about her than you.

Again, best wishes to you as you go forward. What an exciting time!