we have lived in streatham for quite some time now and i would say it's improving all the time. Lovely (child friendly) cafe's, pubs and restaurants popping up all the time at the moment. There are plenty of families and family activities in the area.
I don't agree with the previous poster who said transport links are bad- with 3 train stations close by you can get into town very easily and buses are very regular and will take you back into wandsworth with ease!
The high street isn't great, it's busy and a world away from Northcote but there is pretty much all you need for a basic shop, there's also a nice farmers market every sunday.
Yes there are pitbulls-but i know for a fact there are pretty unruly dogs running loose on wandsworth common too!
For the extra space a growing family needs streatham is perfect. I hope you have a good move!
p.s-i've never seen a crack house-obviously not looking in the right places