Assuming the SJU flight is on time you should have enough time but you can't dawdle until you get past TSA.
AA isn't always the fastest with delivering checked bags, usually 20-30 minutes in my experience. Usually MIA is fairly good about Priority bags but don't count on it.
Assuming 30 minutes you're now at 2 hours to departure.
Depending on which carousel they deliver to you should be fairly close to the BA check in desks when you head upstairs, being Gold gives you access to the Priority line for check in. The longest walk I've had on an AA to BA transfer has been about 20 minute if my bags come up at the farthest North end carousel. Assuming 20 minutes you're at 1:hr 40 min. As longer as your paperwork is in order you should be done in about 10 minute so you're now at 1:30. Unless there's a complete TSA meltdown you'll be through in 20-25 minutes with another 10 minute walk to the transit and a 5 minute ride to the satellite.
It's could be tight but still workable..