Mechanic Misrepresented And Waited Out A Warranty

Location: Iowa, USA. Within the last year I bought a used 2017 Nissan Murano. I was in dire need of a car and didn't do as much research as I should have, so I would later learn that the transmission on these vehicles is notoriously awful. So within eight months it crapped out entirely and needed replaced. I bit the bullet and paid about $8k to get a new (used) one put in. I was told it had a 12,000 mile warranty when I asked about it. It took roughly two months for them to do this

Ever since they put the thing in, it never worked correctly. Within a month I had to take it back in and was told the programming was off and they needed to get someone to do that for them. This took them about a month to get done. I got it back and had it for nearly a month when it broke down again, this time they said it was a sensor not working correctly. These have all been covered by the warranty so far. Now it broke down yet again within a month. They called today and told me that the transmission is busted and they would need to swap it out again, and that the warranty was actually for 90 days from installation, so I'd have to pay the whole thing over again. I have never had the car for more than a month since all of this started, they constantly dragged their heels on getting the car back to me when I brought it in, never having it back sooner than a week and a half, usually about a month or so, and now they're telling me the warranty is gone when I was told 12000 miles.

They won't identify the provider of the part and they are saying that the provider is refusing to do anything since the 90 days is up. But I've brought the car in numerous times during that 90 days, and it seems like they essentially slapped tape on to keep it running til that warranty ran out.

Do I have grounds to sue to be reimbursed, or at the very least have them cover the cost of actual repairs at a more honest shop?