I wouldn’t say you’re wrong in not sharing your phone password, but for her it probably feels live revoked privilege/access since she used to know it before. Did you not worry about privacy back then or is it because she directly stated she wanted to read your messages (vs being a vague possibility before)? If she only wants to know more about what’s going on with your family maybe you can make more effort to tell her about that?

At first I didn't care because I had nothing to hide. But it's getting uncomfortable now.. We did have an argument recently that was not related to this but she did bring up a conversation I had with my sister. Not to get into details but she said I made her (my wife) look bad to my sis. Which is kind of true but it was totally intentional.