cheaper parking is in an open lot at the end of hammersmith grove, right on the roundabout. Hammersmith grove is one way north to south so requires a bit of fiddling about to get on it but the car park is much cheaper than broadway centre or kings mall.
no need to trek to ravenscourt park for swings - really nice clean good playground in the middle of brook green (5 mins walk up the shepherd bush road from hammersmith roundabout, on the right), half of it is for under 2s and has swings, cubby houses, little slides, sandpit etc.
Similarly although shops in hammersmith nothing to write home about, 5/10 minute busride from the broadway takes you onto ken high street, there is everything there shopping wise, including huge zara right at the far end. and entrance to holland park the closer, hammersmith end of the high street, good for a toddle around chasing squirrels. And beside the entrance to holland park is a big ASK restaurant which is super kid-friendly and has no objections to one year olds throwing plates of pasta on the floor.
alternatively for lunch, between hammersmith and the start of ken high street is olympia (the exhibition centre) - in one corner of olympia by the railway tracks there is quite a nice new-ish pizza express your dh could have lunch with your ds, also without worrying about food falling on the floor etc - v kid friendly and smoke free. That is about 5/10 mins walk from the brook green playground.
anything else you want to know just ask - was my stomping ground for about 10 years!