second the vote for Fish and Fritz, wander around the Quay area and you should find it quite easily.
For a nice, special birthday lunch try the Manor Hotel at West Bexington - half way between Bridport and Portland, on the coast path. They do very nice lunches in the restaurant but have a cellar bar room with great views into the grounds that is open to the public - ring first to make sure they don't have a wedding on as you are quite a big group really. The food for the public bar is the same as the restaurant, and its scrummy - gorgeous dishes, but pub prices. They don't advertise as being family friendly, but have got some lovely staff, high chairs etc, and have always treated DD (aged nearly 2)like a queen when she visits. There is a playground area in the grounds too, suitable for the bigger kids, and normally some horses in the field nearby to look at, and child portions - a few of the normal FF & chips etc, but also child sized versions of the grown ups food - delicious!
Then you can go for a stroll on the beach afterwards, or around Abbotsbury, or drive back he other side of Bridport and work off your lunch by climbing Golden Cap - the stonebarrow car park has a lot of space for playing ball games etc, and some nice coastal walks suitable for pushchairs...
We're getting married at the Manor next year and feel quite confident that our dozen or so guests between 0 and 10 will be well looked after. Every time we go over to see about the arrangements we've taken some friends or family, so our group size has been about the same as yours and each time its been lovely.