chocolateandcocktails001 I don;t think you are being unreasonable at all.
You are insecure because he has dated you, broken up, got back together and doesn't seem to want the kids, who are almost teenagers, to know he is in a relationship with you.
It kind of sounds like you have different expectations of the relationship.
The card is a roundabout way for you of saying, You mean a lot to me and we are dating, and you want his kids to know, because that is a sign he is 'serious' about you maybe.
He didn't exactly lie, "On Sunday I asked if the kids had mentioned the card. He said they hadn't." They didn't mention it because he had moved it so they didn't see it.
I can understand why this makes you insecure.
What you do with all this is up to you but you put your heart on your sleeve and he isn't as open with his family as you might expect him to be. That to me is the real issue.