What rights or recourse do I have regarding a dealership and faulty car repair?

You right that the same part was later damaged as the dealership damaged and that the dealership had made a poor or low-quality repair. You could potentially get from the dealership compensation for the degree to which the damage they did and bad repair caused additional costs--beyond those you would have paid for the 2nd accident anyway.
Examples: 
1) The 2nd accident caused $1,500 of damage. Based on the repair shop's professional opinion, the poor quality of prior repair and the use of bondo made the damage worse than it should have been, and had the dealership not damaged your car, or had they repaired the damage properly, the damage from the accident would have been less and only cost you $900 to repair, you could potentially recover $600 from the dealership--the additional cost they caused.
2) On the other hand, say that the repair shop says that the repairs from the accident would cost $1,500 not matter what--that is, what happened at the dealership did not increase your costs or losses. In that case, they dealership owes you nothing, since what they did had no real effect and cost you nothing.
If the dealership did cause you money, present them evidence of that: e.g. some written description or documentation from the repair shop, photographs of the damage, etc. Ask for the money they cost you. If the won't voluntarily pay, however, you'd have to sue; to win in court, you have to bring people in from the dealership, with any appropriate documentation, to testify in court so as to convince the court of the amount of money the dealership cost you (you need experts, like repair shop employees, to testify; without expert testimony, the court will not even listen to you on the subject).