First Serious Relationship

I met this guy 4 years go and started dating a year later off and on due to his work commitment. We got back together 6 months ago and things have pretty much stabilized. He is 22 years older than me, a divorcee and 2 teenage children. I am quite a matured person myself, so I am okay with that. He never talked about his past before, and I didn't ask him because I wanted him to tell me himself. I became very curious and started to look into his families through social media. I found his ex-wife and children. They knew I checked on them from Linkedin. I thought it didn't matter, until recently my boyfriend opened up to me and told me about his past. He said he would love to introduce me to his sons and ex-wife one day. I got anxious since then. I feel embarrassed and scared of what his reaction would be if he knew I am checking out his families behind his back. Somehow I also got the feeling his sons and ex-wife might have had told him about me checking out on them. What should I do if one day I really meet them face to face? I feel so awkward and embarrassed.