Both Nemo and Artis (Amsterdam Zoo) are to the east of the Central Station. Both within walking distance, although you may prefer to use public transport, depending on how old your children are and where you are staying. We haven't visited for a while but we always used to purchase a 'strippenkaart' - multiple journey ticket which can be used on buses and trams. By the way, children aged four and over used to have to pay on public transport, not sure whether this still applies.
As for the red light district, just don't make a 'thing' of it if you do happen to find yourself walking through.
Amsterdam is an odd choice of destination if you have a morbid dear of canals! Water is everywhere in Amsterdam - a lot of the streets are canal banks! Anything ending in 'gracht', for a start. There is absolutely no need to fall in, though, and a canal cruise is a good way to see the city and learn about its history.