Hi,
I've done sort of DIY myself.
Only me and the wife go now because the kids have other interests. We're off again in April.
If I was doing your trip, I would make the first week a travelling trip not based in any one location, and find hotels on the way.
Douz has a very nice, clean but basic, hotel, Vent Mars (March 20) (email: hotel20mars@planet.tn) nice for a one or two night stop-over, it is right in the centre of town next to the market square, the market is a great place to visit and Douz is the "Gateway to the Desert", a short trip out of town will take you to a camel station where you can go on a camel ride far cheaper than you'll book from the tourist resorts.
From Douz you can explore various interesting desert places including Ksar Ghilane, Matmata or Tataouine; it is very easy to travel indepently in these areas using the louage and taxis. If you want a higher standard of hotel then there is the tourist zone where you can find very nice 5 stars. There is something very special about sitting drinking coffee at dusk over-looking the market square in Douz. This might sound a little daunting but it is easy to do and if you book from a northern resort you'll still have the long road trip to do anyhow.
You can even rent a room in the hotel used in the Star Wars film, pretty basic but an experience for any SW fans. I've never been on the Red Lizard train but I've read mixed reviews, some love it, some say it is too expensive for what it is. Sfax is a good place to break a journey for one night, some nice hotels, and not many tourists, one of the many medina's where you'll not be hassled, hang on to the kids though it is easy to get lost. El Jem is then just up the road a little.
Don't rule out the Ile de Djerba, Houmt Souk has some nice hotels, we stay the other side of the Island Aghir, again, less English which makes it seem more like a holiday to me.
Also bear in mind, as a family you'll be able to eat cheaply away from the resorts. Pasta, chicken and chips, cous-cous, with meat and/or vegetables, etc will cost less than £20 for the six of you, and that will include a starter, bread, harrisa, olives and bottled water.
If you would like some specific info mail me from my site,
http://www.4x4-travel.co.uk
Kevin