Seeking, I totally understand how you feel.
I give him credit for being sober for that long, however, if you don't feel you can be honest with him about how you are feeling, that isn't healthy for you. Those bottled feelings build up inside and end up affecting your thoughts and behavior towards him because distrust is building.
The fact that you know he is being a little dishonest with his kids about his relationship with you would hurt me too. He has every right to disclose what he wants to his kids, but to lie about the relationship? That's certainly disrespectful to you. It doesn't feel good to feel like you are a secret. I've been there. And I ignored it, even though it bothered me; I wish I hadn't.
When trust has been broken in a relationship it is one of the most difficult things to rebuild. It takes a lot of commitment on both parts, and mostly HONESTY. You are not seeing that completely. Until you do, you will always question what is going on. It's going to be an internal roller coaster of emotion building inside again. And didn't you want to get off of that?
You should not feel like you have to walk on eggshells with your partner. That is not a sign of a healthy relationship either.
I'm sorry you are feeling this way though. If it's possible to have a rational conversation with him, you need to do that. There is no reason why you shouldn't be able to ask him why he's not really telling his kids he is with you. Not in an attacking kind of way, but in a normal, two adults sharing their feelings kind of way. Do you think this is possible?
If you don't, I would put some thought into your feelings about the situation for a bit.
Hugs.