www.naturarte.pt
Nice, very very flexible and friendly, great with kids, speak english too. BUT not near algarve or lisbon, in the countryside by the sea between the two.
www.vilabicuda.pt
Fab, littlestar stayed and had a fab time, very child friendly, houses or small studios on a nice site with coffee shop, small supermarket, restaurant etc and a creche, two pools, 5 mins from beach, cute town nearby. 20 mins outside lisbon. they will provide stair gates, high chairs, babysitters etc.
i live here, and have been searching in vain for a child friendly villa to rent - its a nightmare, no one seems to have got into the child holiday market here yet.
never visited algarve with the kids, so cant help you on that bit, sorry
hth x