Hi,
The way you are thinking re full lifejackets for the kids makes sense for the reasons pointed out before they will put you face up in the water.
Buoyancy aids are fine if you can swim.
I don't know what previous experience you have sailing but i would strongly recommend joining a local club and also doing the RYA training courses which will teach you what to do. More info here:
http://www.rya.org.uk/Courses/dinghiesmultihullskeelboats.htm
The kids can also do the courses and will give them an understanding of the sailing world. You will perform the skills you need re capsize drills and righting an inverted dinghy.
Another important thing to remember is the type of clothing you wear depending on where you are going out and the conditions. There are many options ranging from shorts and t-shirt to wetsuit, steamer and then drysuits. Jeans and wooly sweaters are to be avoided at all costs because they become waterlogged if you capzise and will try to drown you.
Personally i would advise you to start off with a local club and concentrate on sailing on lakes until you have built up plenty of experience. Lakes have edges and if it all goes wrong you are not going to drift for miles, clubs will also have rescue boats out or on standby to help you if you get stuck.
As for costal sailing you have many more things to contend with re tides, currents, eddy currents again these are covered on the RYA courses and would advise you not to go out on the sea until you really have some experience, righting a capsized boat on a lake in a force 3 is easy, on the sea with swell and waves etc it's a whole different kettle of fish the weather and wind direction can also change very quickly on the coast. You can sail out quite easily with an offshore wind, getting back is very hard if you don't know what to do. Also, i would not consider sailing on the sea without a full wetsuit with spraytop for wind protection.
You also have additional things which you need to carry at sea like flares, an anchor, compass etc which are important.
The above is all from experience, i have come to the aid of quite a few ill prepared people on costal waters in boats they have bought and then just taken to the sea. Personally i doubt you will be one of them as you are asking questions
There is loads more than the above but a good book coupled with joining a club, getting experience and training will lead you into a sport which is very safe when you have the knowledge.
What dinghy did you buy?
Jon.