Since I do not have any kids I can't really talk about that. But players from our playgroup have children and every single one of them prepares a card pool for their children. I found that very odd but obviously it is something the fathers share. They plan to introduce their kids to the game and with time pass down the collection (some already taught them the basics). I find this strange because their kids do not need to show any interest in the game in the future. (I have no experience parenting and I was never in an environment with kids growing up (I'm the youngest). This is probably why I do not understand this.) I guess that one reason for this is that the parents want their kids to be able to play with them.
Introducing your kids to something you love is probably something good. If I would ever have a child I would probably want to share my passion as well. On the other hand wanting my child to play Vintage (my format of preference) is something that I can't even imagine happening. Magic players tend to play Magic for different reasons, they like different aspects of the game (my ex plays mostly Standard and we are totally incompatible Magic players). If the kid even starts to play Magic, he may be interested in something totally different ? The game will most probably be different in 5-10 years or so as well. Shouldn't you as a parent introduce the kid to the game, show him/her the intricacies of the game and different formats and let him/her decide later? (I did not really go through real childhood either so I have no idea what 7 years old do or think about)
I always expected that if by a chance I would ever have a child and Magic would still be around it would be the kid that would come to me asking 'How do you play this game/What is this game?'
Otherwise I really envy you and your kids^_^. My parents weren't supportive of any of my hobbies until I managed to qualify for Worlds Championships. (After 15 years of playing Magic my parents gave me a booster pack! That was actually pretty awesome)