Hi Magda,
A couple of observations based on my few years here with my wife and children:
1. Treat mozzies as a potential problem. They won't carry you away or anything (it's not quantity that's the issue), but as someone who employs a couple of hundred staff in Bali, I can tell you that Dengue fever is an everyday occurance. We probably have more mozzies in Northern Australia (and we have Ross River fever), but disease is nowhere near as prevalent as here. Don't stress too much about it, but certainly use nets, keep windows closed at dusk and all the basic good practices people have suggested. Wouldn't have a clue about DEET - we use Aeroguard on the kids (just as we did in Australia) and it seems to work Ok.
2. Obviously it's horses for courses (I don't want to start a "holy war"), but for us Seminyak is just a bit noisy and party-oriented. With 12 year olds, we prefer the relative peace of Sanur, Jimbaran or the Bukit. We planned to try Seminyak before we came here as a residence, but I'm glad we didn't go that way. Of course, if you want a night out at a restaurant or club, that's a different matter . . .
3. We bought a veritable pharmacy with us when we came, and needed almost none of it. I do bring cold & flu tablets back whenever I visit Australia (local brew is pretty industrial strength), but that's about it. Everything else is here pretty much.
4. Balinese LOVE children, so prepare for some serious spoiling. Also, Balinese will rarely say no to a child's request, and in my case my kids learned that pretty fast.
I hope that this helps.
Mike