Hi Mel8
Sorry taken me a few days to notice this - welcome to Madrid!
Have sick DS so will keep this brief:
Have you discovered St George's Play group on Wednesdays and Fridays?
Have you been to Sticky Fingers playgroup on Tuesdays and Thursdays?
Both are full of expat mums - many permanent like myself but also many new and short postings here. We all understand how tough it is with small child and lack of language so I am sure you'll find some like minded mums there. My two are at school already as they are the ripe old ages of 3 and 5! (We do so love to start them early here :-) )...
Also, there is the American Women's Club which is excellent as not only do they have a full time club house open Monday to Friday to drop in those days you are struggling to cope (EVERYONE there understands, trust me) but also they have a Mums and Toddlers group that meet once a week and like to go out to do activities when the weather allows.
Finally, for the grown up time there is the INC (International Newcomers Club) which has local coffee mornings and then a monthly meeting and you can take babies with you under the age of 1year.
So now for the question I should have asked at the beginning - where are you located in the city? I am afraid we live out in the countryside now so can't offer to meet for a coffee without pre-planning but am happy to do all I can to help you find a ton of friends and get to enjoy Madrid, especially now the spring has arrived.
Contact me offline as well as online any time.
Hasta pronto