You must be a very good person to consider the feelings of his mother, and indeed him, regarding his first teddy!
Seeing as the engagement ring belonged to his mother and sadly your marriage didn't happen, by all accounts you should return her engagement ring: not because you feel you must but because you are a good person. If the situation is difficult write a little note, perhaps something like; I want to return this ring to it's rightful owner_regarding the teddy, try; I felt it only right to return this symbol of many childhood memories. Sign off with, Regards and your name, and post them.
The promise ring is a little different, and this is your personal choice as we don't know how you really feel. However after two years, perhaps you should pawn it and use the money to treat yourself in a way that you'll remember, and one that brings a smile to your face. Good luck.