As Lisa say, Speyside is good for your diving, but it doesn´t fit into your other specifications, it´s in the north of Tobago, no supermarkets just smaller local shops and not many restaurants. For you Speyside is good but for you wife Crown Point area is the best choise.
There are no hotel with placed direct ON the beach, it´s not allowed in Tobago, they are just nearby the beach as all beaches are public except for Coco Reefs handmade beach and Canoe Beach.
I don´t know any hotel with a pool adjusted for a baby or smaller children, so whereever you will stay, she will need to keep an eye on the baby around the pool. But maybe some with smaller children can give you more information about where it´s best to stay.
I would say that the best is to choose a hotel or a self-catering in the Crown Point area where your wife have more choises during daytime and go with the diving tours for your diving at diffferent areas around Tobago. Its´a small island yo know.
There are differnet hotels there, both small and large ones, mostly of them do have AC, but that´s something you can check out here. There are also many restaurants in the Crown Point area, both smaller places and very good ones. There are some smaller shops and mini-markets with food too, and the supermarket Penny Savers in Canaan is only a few minutes away with car.
The airport isn´t busy so there aren t much noise from the aircraft, not even when a 747 arrive.
Ýou find a nice public beach as Store Bay Beach wich also have beach bars, local food and a local restaurant and they also have small huts for different things for teh visitors. Change rooms with showers and toilets, and they are working!
The beach has sun chairs for rent and there´s always 4-5 life guards on duty. No reef in front of the beach so the water is clear but it´s not shallow. Very nice sand all ove. Divers also use to be outside this beach but I have no idea how it looks down there.
Pidgeon Point Beach is a few minutes away with a car, some small huts with clothes, a beach restaurant and this beach is on one side very shallow becaus of a reef, the water is very warm here. On the other side, Bucco side, more breze here and the water isn´t so warm here.
Ouside Pidgeon Point you also find diving centres, I guess you can find more info on that here at myTobagoinfo. Thay believe operate both via boat and by car.
I believe you will get all needed information here, just ask again after been checking all other info here.