I have 2 kids age 3 and 5 and I can honestly say I am not going to kickstart a game on their behalf anytime soon. By the time they even find out what kickstart is and could nag me to fund something, the game would have to also convince me that it is worth the investment.
The only way you are going to drag the parents into this is to have some kind of educational or “life experience” hook. Even then, there is so much free stuff out there that we don’t have time to get to, your product would have to be truly exceptional.
I don’t think there is any kind of marketing you can do for your game, especially at this point, that would help you out.
In the future though, your best bet is to think of the parental hooks you need to design into the game, use those hooks as advertising bullet points, and then find those parents groups, organizations, etc and advertise to them.
Alternatively, you could go the Angry Birds route. Those kinds of games practically advertise themselves.