Hi OP
I am married to a tunisian man and want to reassure you that you will be absolutely fine in the resort/Hotel.
We stayed in a hotel close by last summer and going back this Easter to see family.
The no go red zones are to the west and south as other posters have stated. You are hours away from these areas and would have no need to go that far.
if you want to do some daytrips youve got the seaside towns of Hergla/Nabeul, the larger resorts of Monastir/Sousse/Port el Kantaoui about an hour and a half south of Hammamet, and an hour to the north you have Tunis capital and Sidi bou Said.
You've also got El Djem roman amphitheatre almost 2 hrs from Hammamet.
As others have said just wear normal beach/summer clothes in the hotel but if you decide to go out shopping or sightseeing cover up a tiny bit more - not just for modesty but also the heat.
Do be careful of the young waiters and entertainment guys trying to chat you up if you are on your own (even with your kids)
The current exchange rate is 4 tunisian dinars to 1 pound and you are expected to haggle in markets and small shops but not supermarkets. You can't exchange money before you go so take some english bank notes and exchange them a little at a time in the hotel for souvenirs etc
If you tip you waiter at the start of the holiday (10 dinars) so £2.50 you will get great service. Also tip a little at the end as hospitality wages are awful.
The chambermaids will appreciate a tip as well and if you have any toiletries you don't want to bring home leave them in the hotel room for the cleaners - branded toiletries are extortionate in Tunisia.
Tunisia isn't for everyone but on the whole the people are kind and generous and love children.
Hope this helps