Anna: I find that the best city guides (well, my favourite) are the time out guides. see if you can fetch one on Milan.
I really hope you'll have a nice stay, Milano can be utterly charming, if it wants... . The worst thing is def the traffic, but by staying at duomo you have two lines out of the three (pathetic I know), and as the city center is quite small it won't be too expensive taking a cab.
Abena, good luck with your move! I don't know much about the area you are moving to (I've heard about the english school though, and it's got lots of lovely facilities if I remember well) and being close to Parco Lambro it's certainly good for your dogs... as I said I don't know much about Lambrate, but there' is a metropolitana (tube) which relieves a lot of stress, as moving around in Milan is a major pain.
Childcare is cheaper than in the UK, and that's because there are asili nidi comunali (run by the council). A place in asilo nido comunale (for children between 9 months to three year old) costs between 100 euros and 400 euros a month, depending on your household income. It's very difficult to find a place in asilo comunale, and you have to put your name down on a set date (usually in february or march, I think) to start the following september. Private nidi are good as well, more expensive (tbh don't know how much) but not as expensive as in the UK. The staff needs to have a proper qualification, so no stroppy teenagers on site. I'm not by any means saying it's perfect, but again, friends feedback has always been very good.
Scuole materne (for 3- 5 and a half) are both statali or comunali and cost 50 euros a year . they are the last bulwark of a once good education system. I'm told it's quite difficult to find a place there as well, but again, my friends with children have never had a problem and have all been extremely happy.
Alternatively you can employ a babysitter, but this seems to work a lot by word of mouth, I can ask my friends if you want!
If your husband is going to work in an english environment, your move will be much easier, I believe, and you might be in touch with otehr english mummies. As I said, I don't think there are many activities for mothers and toddlers. But there's lots of socializing in giardinetti and parks. And there are also swimming lessons for little ones in almost every swimming pool in Milan, there's a puppet theatre etc etc.
I'll be happy to answer any other question. There's another english mntter who lives near milano, brangelina.
I'm feeling all protective of you now, I do think that moving to Italy can be quite shocking for an English person (and certainly also the otehr way around ), I really wish you all the best!