I know all about this one!!
Don't take the car. Absolutely no need whatsoever, all you need is a pushchair or backpack. If you have a choice, don't take the ferry - it's flat-bottomed so's to be able to get in within the islands, but has to go through some quite big Atlantic seas to get there, and for those who get seasick ... Take the helicopter from Penzance, it's noisy but only 20 mins & brilliant.
Tregarthen's on St. Mary's is pretty family friendly (does high teas etc.) if you don't mind your group bringing the avg age down by 40 years (actually that goes for the whole of the Scillies). I've heard great things about the hotel on St. Martins, but it's much posher. I wouldn't do the Tresco hotel with little children, bit starchy I think, but you could go over to see the gardens.
You can walk everywhere. Roads on St. Mary's are quite busy, on the other smaller islands there are wide concrete pathways done I think in WWII so it's like walking round a park, plus coast paths. Beaches everywhere, and it's all entirely civilised - shops all stocked with whatever you need, etc. Water - don't know, it's the Atlantic but sheltered - certainly mine paddled dawn to dusk. Don't expect any nitelife.