Welcome to the forum!
I don't think there are any AI's that include diving.
as far as experience goes, you can't just tell a reputable dive op your experience, they will require you to show your C-card, yes, but they will evaluate you in the water the first day or so to see whether or not you need "baby sitting" ... sounds like you shouldn't. usually once you have been 'approved' by the DM's, they don't require you to be right up their butts too much, just stay within eye shot. Your DM should cover his requirements in the pre-dive briefings.
Dive with Martin has always had very good rates and is a very good dive op, (not sure if they are doing cash only still or not, but always good rates). Other dive ops to check into are Blue Angel, Bottom Time Divers, Living Underwater, Dive with Alison, ScubaTony & Tres Pelicanos, you'd have to get quotes to see if they fit into you budget.
Most dive ops will pick up at most hotel piers, from downtown south, so diving with an "in house" dive op is not necessary. Again, check with who you are thinking of diving with to make sure they will pick you up, otherwise you might have to go to the "Caletta" (the little harbor about 2 1/2 miles south of town, that most dive boats harbor at & some dive ops operate out of) to catch your boat.
budget minded hotels: Hotel Cozumel is reasonable and has AI options. Blue Angel offers free daily breakfast on dive days , Hotel Barracuda, Casa del Mar, Casa Mexicana, Tiki Village are all budget minded places.
The Fiesta Americana has recently been renovated and I THINK they do AI now. The Sabor and Occidental Grand are popular AI's, but quite a bit out of town, $20 U.S. cab fare (min.) one way from OG to town, probably closer to $15 U.S. for the Sabor. One note, not sure if Barracuda is still a good place to stay, I haven't heard much about it lately, folks that used to stay there always gave it good reviews, maybe someone else can chime in about it.
AI is not super important on Coz, unless it's just what you prefer, as there are many very good budget minded places to eat on the island covering many types of cuisine, and if you stay at places close to town, Hotel Coz, Casa Mexican, Barracuda, you could save on cab fares by walking (Barracuda and Casa Mexicana are both actually in town)
I think usually flying into Cancun and doing the "bag drag" is cheaper, but takes up more of your day. You just have to check air fares to both Coz and Cancun and see if by the time you figure in transfer for both of you to and from Playa del Carmen, and the Ferry both directions is worth the money you save over flying directly into Coz. I think, $20 U.S. per person(ish) from Cancun to Playa on a bus & it looks like ferry fees are around $11 U.S. per person one way.
Transfers from the Coz airport to you hotel are handled by government controlled shuttles, that are part of the taxi system. it can cost up to $20 per person depending on how far south you are staying on the island. We stay at Blue Angel, it is about 1 mile south of town and our transfers from the airport (which is on the north side of town) are usually $16 U.S. for the both of us.
Hope this helps, have a great trip!
