If he was the one for you, then you would know it and you would not even have to ask about whether his behaviour was normal.
The best relationship advice I ever had was that you know when you've met the right person because you just 'click' with no effort or mental acrobatics!
3 weeks in seems very early to be introducing him to your dcs and wanting family days out.
Does he have his dcs at the weekend and feel at a loose end during the week?
You have reminded me of someone I knew just about the time of my 21st. He was in love with my friend after 2 dates. Flowers, booking holidays, the lot. She found it a bit much but mentioned to him that I quite liked him. So we had a chat on the phone and he seemed ok. he turned up at my 21st party 2 days later with a huge bunch of flowers and massive card 'to my girlfriend on her birthday' - you can imagine my parents and all my friends as I protested that I hardly knew him!
So I also gave him the brush off. less than a month later he announced he was ENGAGED to someone my friend and I both knew!
So, some people just want full on romantic relationship stuff from the first look.
You don't sound like you do. So keep him at arms length, don't introduce him to your children till you are sure of where the relationship is going.
If he starts saying 'why can't I meet your children/friends/family' etc and putting pressure on you then thats the start of the nightmare boyfriend and you should run like the wind.