Well, you are completely wrong on the prices and availability of rooms. Also almost everything at that price point is going to be all inclusive, which you may not be pricing in. So if you aren't a heavy drinker all inclusive /resort probably doesn't make sense for you, since the main appeal for those is to drink your body weight in alcohol and be waited on hand and foot without worrying about the bill. Sounds like you will barely even be at the hotel and maybe your wife will enjoy relaxing.
I'd go the airbnb route and maybe splurge and get a private chef one of the nights for fun. The rest of the time you can just drive wherever you want, there's also day passes for beach clubs all over the place that are all inclusive if you wanna do that vibe one of the days. (You can hire a driver or rent a car, although the insurance is a bit wonky in MX so you have to put a 10% refundable down payment on the car if you dont buy their premium insurance)
Xcaret is a huge outdoor theme park with all kinds of incredible stuff. Good for 2 full days or 1 really long day.
Take the ferry to isla mujeres and bounce around a bit and then go back from playa del Carmen, then maybe do a day trip to the ruins. I'd skip tulum with the fam tbh. There is no shortage of stuff to do in the riviera Maya. Everything is cheap as fuck, and it's mostly safe if you aren't being a shithead.
For a family of 4 for a week in comfortable digs you should be able to do it for 4k including flights. You can cheap out and do it for 2500 and the sky is kinds the limit of what you can do, you can spend 10k it just won't really be worth it.