I'm camping again this summer for the first time in 8 years! The weather better be nice to me.
If you have a smaller tent, that you have to kneel down to get into, then a cheap doormat (one designed for outdoors) is essential so that you can kneel down on it to get into the tent rather than on the wet ground.
If you tent has fitted groundsheets, either throughout or just sleeping compartment, then it can be useful to buy a cheap extra groundsheet to fit the footprint of your tent. this means that
a) when you pack up in the mud and rain the bottom of your fitted groundsheets are reasonably clean and dry for rolling up in the tent bag - even if you have to get the tent out at home to dry out it is a whole lot easier to do if the fitted groundsheets aren't that muddy. The cheap loose groundsheet is much easier to hose off and dry than one fitted to a tent.
b) your fitted groundsheets are likely to last longer and not get worn where they've rubbed against a stone etc.
Take something to carry water in - even if it is just a large 2-4 litre bottle of mineral water. It stops you having to go to the tap every time you need to boil the kettle or give dcs a drink.
It might be helpful to have a plastic box just inside the door of the tent and make every one put outdoor footwear in it to stop mud and wet getting everywhere.
Wetwipes/babywipes - lots of them - quick cleanups without having to trog to the loo block.
Groundsheet or waterproof picnic blanket for sitting on outside.
Either lots of old supermarket plastic bags or a roll of bin bags. You will get through loads more than you think as you will probably want to get rid of rubbish every day rather than having it mouldering in a corner. They are also good for stashing wet/muddy clothing that you are not going to do anything with till you get home.
Pillows - I know they aren't for the camping hard-core but I think they make all the difference to a good nights sleep.
Matches, a couple of spare tent pegs, tin opener!
Oh and if you tend to wake up when it is light then you might like to think about a sleep/eye mask as the tent lets in loads of light and dawn is ridiculously early as will the waking times of your dcs be!. The birds can be incredibly loud too and will compete with your children for the privilege of waking you up at silly o'clock !