To be honest with kids I would book into a cheap hotel and get some sleep.
The best value and really close to the airport is Premier Inn. You won't have to collect luggage because it will go straight through, if you are all UK passport holders you will get an automatic visa stamp in your passports at immigration and could be in the hotel and in bed by 1am.
The hotel has a free shuttle bus service but to be honest a cab will take 5 minutes so I wouldn't bother waiting for the free shuttle bus - a cab will cost around 25 dirham (£4 or so) and that includes the standard 20 dirham pick up fee.
You will already have your boarding passes from your first check in point so can just go straight to departures security the next morning and into the departure lounge. Allow 90 minutes for this.
Leave the Premier Inn at 7.30am and you will all have had some sleep.
Spending 9 hours in Dubai airport would try most folk but with kids I wouldn't even attempt it.