So yea you should demand that they reimburse you for your monthly payments and demand a free extended warranty. You should also demand a free car of your choosing
Honestly the flat tire thing is bad but it sounds like they are doing what they can. They took the time and effort to have an expert fly out straight from BMW. It's def not unreasonable for you to voice your displeasure at your car being left in the condition it was... but I think they will laugh at you if you ask for your car payments to be made or to get a $4k+ warranty for free for nothing more than a minor inconvenience.