1) I +believe+ that for online bookings you have to be a Flying Blue member as otherwise you won't have the Weekend fares offered. The way it works is that you log in, and in the section where you indicate who is traveling you chose yourself and click that you have the Weekend card - and only then are weekend fares offered. If you don't log in, you cannot select the Weekend Card option, and you'll only get offered non-weekend fares.
2) For your kids: not sure you can buy a Weekend card for children <2 years? If there is, sure, buy them one - but that will mean that they'll have their own seat.

The AF system is quite cumbersome in that everybody has to be on the same fare - it's not like SNCF where there is an individual price for every passenger according to their rebate status, all in the same booking. So for AF, if you have one adult on a weekend fare, one another without weekend fare, one kid with a Carte Jeune, then you have to book them separately and then call in to link the PNRs so that you can sit together.