Sacrificing your right to privacy and letting him run all over you without considering your feelings is absolutely not the way to handle this. What he is doing is not only rude and unacceptable it is a form of abuse. You are entitled to your own privacy as he is, just because you are in a relationship doesn't mean he can go through your personal belongings if you don't want him to. You deserve respect and you're not getting it. Your coparenting relationship with your ex is your business and not your fiance's. Talk with him seriously about your need for respect and personal privacy. Try not to sound accusing... he may not realize that what he is doing is wrong - but be firm and insist upon what it is that you need him to change. If he continues to ignore your requests and your feelings then you may want to consider that he's not respectful enough to be the kind of man you want to be with.
Most time over reactions like that mean u might want to go threw his phone! When my husband gets crazy I get crazy rite back then he sees how silly it is and he stops! So him a little crazy and maybe he will settle down!
The more you get upset the more he will think you have something to hide. Let him look and he will see there is nothing and stop.
Trust is huge in a relationship it's a fine line that can be crossed. It sounds like your doing everything right in being open about everything and he needs to understand you will always have a connection to your ex on some level because hes your daughters father. Your right you need your space and he should trust you I would tell him how u feel about it good luck
Try to sit him down and tell him exactly what you just posted. Tell him tht part of you life is gone you and your ex have moved on to new relationships. He hve a gf and a baby and you and your hubby to be hve each other your daughter and a bun in the oven. Tell him you want the same respect tht you give him! Wish you both the best and congrats on the engagement!