Hi Mick,
With a family, I'd definitely stay in an apartment if possible (see my comments and recommendations on the post headed "Please can anyone help this newby?" There are lots of choices re. apartments in Bangkok.

I don't know about apartments in Pattaya, but another poster Denise davden made recommendations quite some time ago.
If you can't find these posts on here, I'd recommend a couple of places in or near Pattaya (personally I wouldn't stay IN Pattaya whether with kids or not - better to stay just out of the town.)
Try either North Pattaya - Woodlands Resort - quiet, with 2 nice pools and lawn area, good restaurant and nice rooms. This place would be good for your kids.
Otherwise, another favourite of mine at Jomtien (south of Pattaya) is Rabbit Resort - lovely Thai villas (upstairs or downstairs) with full facilities, nice pools, a 'boutique' type of place - small and with a bit of an exclusive feel, right opposite beach (has a section for Rabbit's guests) and very good service. A family villa there probably similar price to 2 rooms at Woodlands.