Just returned from my first trip (gulp) with the DTs and thought that I'd pop down some random thoughts in case it helps someone in the future.
I went with my parents while DH went skiing (lucky bugger, he did get rain on Thursday, I tried to be sympathetic but it was difficult...) so we had a 3 adults:2 children ratio which I highly recommend.
We stayed at the Apartments Atlantico in the centre of Funchal, in a duplex. Great location, very nice apartment, well equipped kitchen, clean, friendly staff etc. Drawback: wooden stairs. Mine were fine, we just watched them carefully, but would be slightly more hazardous for younger ones.
The Madeirans are very welcoming of small children - their food always came first, nothing was too much trouble, restaurant tables were moved for buggies, to accomodate high chairs and our buggies had their own valet parking several times! DT2 is very blond and got her hair tousled several times a day even on the street and in shops so don't get freaked out about that.
All the restaurants have familiar things like spag bol, omelette and chips etc. on the menu for small ones, plus the local fish espada is white, chunky and not very strongly flavoured and is available everywhere.
Good activities: St Catherine's Gardens (on the hill above the marina) has a children's playground at the top. New ships in harbour everyday, leave again about 5/6 at night, having helpfully sounded their horns so you can show the children. Swans to feed in the Municipal Gardens (opposite the theatre), Cable car up the mountain although the step-free route through the Tropical gardens is hell with a pushchair unless you have an all-terrain buggy with you, which is unlikely on holiday. Visit the fish market and see all the fresh fish on display, take them to choose their own fruit to buy from the general market (same building). On a rainy day visit the Natural History museum. It has an aquarium (about the size of a living room, but of course they loved it) and a very Victorian display of stuffed birds, sharks, big fish. On the seafront there is a wide promenade separated from the traffic by grassy areas so it's fairly safe for toddlers to walk for a chance to get out of the buggy. Same inside the parks.
If you go up the mountain, go past the entrance to the gardens, past the crazy wooden sled people and follow the little parth which curves around under the church to a square with lovely handicraft stalls and you will see a snack bar, up some steps. Bear with all this climbing and cobbles, best espetada (local BBQ'd steak on a stick speciality) we had anywhere and incredibly welcoming to the girls.
High chairs were few and far between, especially for 2, but we took Baby Polar Gear Go Anwhere booster seats and found them brilliant. Changing facilities also very scarce but toilets in restaurants and cafes always very clean. I bought pull up nappies (more on nappies below) and found stand up changes in a cubicle the easiest. Good clean changing facilities in the cable car stations top and bottom and in Mar Azul, a lovely restaurant in the marina which also has tanks of fish and crabs/lobster - fun to look at.
I found nappies easy to buy in the supermarkets, but not in smaller markets or in pharmacies. However, they almost always stocked them in very large packs (80/100 nappies! - even with 2 I would have struggled) so if you e.g. only use them at night, it might be worth packing your own. Pampers is the leading brand (didn't see anything else except supermarket own brands) called Dodot there and the different types are called different things but easy to identify with pictures on the packet. Also found it difficult to buy babywipes without alcohol or perfum - wish I'd packed my own.
There is a new shopping centre called Dolce Vita, everyone knows of it. The ground floor has a big supermarket called Pingo Doce, sells lots of nappies, baby bottles, dummies etc. On the middle floor behind the escalator there is a soft climing frame and slide.
Hope someone finds it useful.