fizzle you may find August traffic to and from Rye can be slow-ish, it may be more than half an hour to Battle, but an early start can help!
The train is great and I also love visiting Derek Jarmon's old house if it is still there, I haven't been for years, near Dungeness.
I love Hastings Old Town. I'm not sure of the distance but a day there has loads for your two dc.
There is the Aquarium, the Fisherman's museum (free) with a real old boat inside the kids can climb on, the Cliff lifts amazing views, the beach with a fleet of real fishing boats on it, fresh fish everywhere, the Jerwood Gallery (not cheap I hear, I haven't been in yet as it sounds pricey), there are two other museums in the town I think, various galleries, interesting shopping, a sweet lot of winding streets to explore, crazy golf near the beach, some really big trampolines, playgrounds near the beach, a funfair, a sweet miniature railway that goes along the Old Town beach, the RNLI lifeboat station has a good gift shop, there are amusements and rides, there's two or three rides for your dc. And general fish and chips etc of course. There is a lovely metal sculpture of a winkle shell that you can put money in and it makes a sound. I visit several times a year as we have friends in the area, I love the Old Town. It obviously is not the Norfolk coast, you have a proper social mix but I don't mind that. If you like looking at Art or even buying it Hastings and St Leonards is full of artists and odd galleries so you can find affordable art if that's what you like. Rye has pricier Art I would imagine.
Bexhill has the gorgeous De La Warr Pavilion and an excellent play ground for free.
You could go to both places by train from Rye I think.
Have a great time whatever you do!