Maybe a little late but I don't agree with most of the people above. You had a contract with TAP for bringing you to a specific airport at a specific time. They did not fulfill the contract and therefore you were forced to make changes, you made expenses and lost time.
Now, I see lots of discussions about EU261, but national law is about compensation for damages and losses. EU261 is only about the compensation for the loss of time, which they express as lump sum depending on the distance of the flight, to keep things simple.
You can ask them for EU261 compensation of 400 EUR, and let them know at the same time that you will go after them according to national law for losses and damages caused by this delay, if they refuse this lump sum compensation. Don't talk about arriving too late in the hotel. Follow up through social media and be VERY persistant. TAP is not great with paying compensation but I have been successful before and you can read in the dedicated topic that other people have been successful as well. I think your chances are rather high to get something, either 400 EUR or the reimbursement of the rental car.
Worst case, a local court will have to decide whether the airline can expect from you to wait 14 hours in the airport if you can do the trip by car in 2.5 hours.