I used to live in Brighton but its been a few years so bear with me.
Peter Pans on Madeira Drive is great for younger kids with rides for the littlies.
Depending on what the kids like there are usually loads of arts and craft stuff for kids too eg there is a drop in place where kids can paint their own cups/ plates / bowls etc so they may enjoy this if the weather is bad.
The beach is shingle and my DS loved, infact still loves, throwing stones in the water and there is a fab free shallow pool for kids on the seafront with a playarea attached. It makes for a really good day out and the kids always sleep well after a day spent there!
If you are in central Brighton there is a park called the Level and this has another shallow pool for kids and a fab playarea. Take a picnic cos the kids will want to stay there all day!
If you like pubs I think there is a Wacky Warehouse type place in Saltdean and Rottingdean just down road has a much quieter beach with fantastic rock pools for the kids to look for crabs etc.
There are lots of great parks in Brighton too - Nizells Park in Hove is great, Preston Park has a great cafe attached and Hove Park ditto.
You are going to have a fantastic time!!! Enjoy!