I think I might be the female version of your boyfriend. I don't discuss my relationships with my dd, never have, and I don't plan on it unless I am seriously considering marriage. If I go out on a date, I leave my house and meet them in another location. I would invite them to my house, IF my dd was in another location. My dd has had her dad walk out of her life, and now my dad (who was the closest version to a dad she knew, even more than her own) is getting married and moving on with his life. She's had enough people leave (my mom and grandmother both dd was close to died within 6 weeks of each other in the fall of 2006) I don't want to create any more situations of loss in her life. (This is just my life, I don't know your bf's reasons, these are just mine).
My life is busy, and if I got a note like yours (not saying there is anything wrong with your feelings, this is just how I feel in my life, and I'm trying to give the other side of maybe what your bf feels like) I would back off of the relationship and possibly end it. I have dated people that wanted me to remind them that I was thinking about them, and I ended it. When I am with them, I am with them and I am devoted and all my energy is focused on them. When I am away and busy, I am living my life, and I am not interested in calling/emailing/texting them just to remind them that I am thinking about them. I am just that type of person. I need my space, and while I am willing to compromise on this issue (because if it were up to me, I would go 2-3 days without talking to a person I'm dating and think nothing of it) I will never be a person that is a more than once a day talker. Once a day is as much as I can give, and I would totally fall for a person who gave me the space to go a couple of days without the how are you, how was your day conversation.
I wish you the best in your relationship. Please don't send that note.
* One more thing. I really don't want you to think I'm picking on you
but when people use the term "how do you think that makes me feel" or when I want to ask this to another person. I try to step back for a moment, and think deeper about myself. How do I feel, is this a reaction to what they did/said or is this say more about me and how I feel about myself.
Let's imagine that he doesn't want his kids to know about you. That he doesn't care if they know you exist. Does that change how you feel about him, or does that change how you feel about yourself?
Just something to think about.