The reason I bought a Mozzie was because it could be sailed either 2 upor solo. In fact the only reason for the initial purchase was so that I could go sailing with my son and daughter. If I ventured out without them I was seen as selfish!!
The very first time we went out a Mirror sailed around us. Now that's really embarassing.
Mind you there were 3 of us on board.
So my suggestion that to keep in the good books and get some extra brownie points is that you take the kids out.
Mid morning is usually a good time so that you don't have too much of a sea breeze. As Col said earlier try it in a lake or bay; Portarlington comes to mind because it is usually pretty flat water and you can reach up and down the coast (within reason).
As for sailing with or without a jib, the jib will allow you to tack easier because you can keep it sheeted until you are well through the eye of the wind. It will actually help pull the bows around and therefore is more forgiving of your learning stuffups.
It will also give your kids some responsibility on board rather than just going for the ride.
Hope this helps.
p.s. wear an old wetsuit to avoid rashes and bruises from scrambling about on the trampoline and bumping into fittings.