I think it's very important that you handle any bad behavior the first time it pops up. If you let it slide, it will only get worse.
For example, this girl I'm seeing saw me texting someone and asked to see my phone because she thought I was texting another girl. I said I wasn't but I actually was. She insisted and asked to see my phone. I told her there's no way she's seeing my phone.
She got all upset and said "Okay. She's leaving." I just chuckled to myself and didn't say anything.
Few minutes after she left, she texted me saying "I can't believe you would choose me over a stupid phone."
I didn't respond to that.
After dozens of calls and texts, I finally responded to her and said "Well, I don't think I can be with someone that doesn't trust me."
She started apologizing profusely and said she trusts me and she'll never question me again. She even wanted to bring me flowers. I kid you not.
She never asks for my phone ever again after that. Imagine if I had given it to get the first time like a little beta boy, she would ask for it every time she suspects something. Refusing after that would be much harder because I would be used to it and she would be used to it.
Learn to walk away early in the relationship or at the first sign of any red flag. It's very important. Don't wait before it's too late or you're in too deep.