We did Southampton to Prague a few years ago, stopping in Cologne overnight on the way down and doing non-stop on the return trip.
We went by Euro tunnel and back on ferry from Calais. Buying petrol or diesel is simple in all the european countries you go through (we went through France, Belgium, Holland, Germany and Czech Republic). Garages are generally self service as they are here, but you may have to pay before putting nozzle in tank. If youve got AA European cover you will be fine, just follow the instructions.
It is compulsory to have headlights on in the czech republic and you must carry full set of spare bulbs and hi-viz reflective jacket in case of breakdown. You must also have a licence to drive on motorways in czech republic which is a sticker you display in the windscreen, ours was supplied by family who live there but maybe you could get yours or at least advice from czech embassy in London??
If you travel on a Sunday through Germany its much easier and quicker because all HGV lorries are parked up and not allowed to use the autobahns.
Our children were older and the dvd players in the car were invaluable! 14 hours is a long time, it took us 18 hours Prague to Southampton non-stop including boat.
It was not my choice to drive, but to visit BIL, was only way as DH wouldnt fly! He has since done fear of flying course and has been to USA 4 times!! Would fly if we go again! Hope this is useful info, DH dictated most of the above!!