We want to commend you and the person who caused the accident for wanting to do the right thing regardless of personal loss or gain. (The question ignores any involvement of insurance companies, and the answer follows accordingly.)
In general, there are two possible approaches concerning how one must compensate for damages he has caused. One approach is to pay for the property’s depreciation in value that was a result of the damage. The other approach is to see to it that the damage is repaired. At times the former is more expensive, and at times the latter is. These two approaches are likely the basis of the following dispute. The Rambam1 writes: If Reuven demands payment from Shimon for the damage he caused by digging two holes in his field and Shimon claims that he dug only one hole, there is a rabbinic requirement for Shimon to swear that he didn’t dig the second hole. The Rambam[1] explains that even though, in general, a partial admission creates a Torah-level requirement to make an oath, here, the subject is land, and, as the Talmud states, Torah-level oaths are not required for disputes over land. The Ra’avad[2] contends that despite the fact that the subject is a field, the nature of the claim is a monetary one, and therefore the requirement to make an oath is on a Torah-level. The Rambam may view payments for damage as a means of repairing the object, which in this case is land, whereas the Ra’avad views them as monetary compensation for the loss. The Shach[3] and Chazon Ish[4] imply that the Ra’avad agrees that when the normal course of action is to fix the damaged object, then the payment is geared to that need.
It appears that according to either approach concerning this fundamental issue, you are not entitled to demand payment to fix the door entirely. This is because the second driver is only responsible for the damages he caused, not for previous damages that you incurred. Regarding depreciation of the car’s (re-sale) value, there is probably little difference between a car with one scratch on the door and a car with two. The possibility that the same, second scratch would have made a bigger difference in the price had it been the car’s only blemish is not relevant. If one severely damages a luxury car and a second person subsequently “totals” it, the second person is responsible to pay only the value of a severely damaged car.
In terms of having him pay to fix the door, you probably do not have a claim. The fact that you decided not to fix the door after the first scratch seems to indicate that the damage does not warrant fixing, given the cost of repair and relatively minimal benefit. In such a case, even the Rambam should agree that one does not pay to have it fixed, and his financial obligation would be only for the diminished value of the car. Is it logical to require an exorbitant price to fix something of little value or to improve it only slightly?
Under two circumstances, however, you could demand the second damager to pay to fix the scratch he made. If the average person would have paid to have the car fixed the first time but you decided not to do so for whatever personal reason, you can now decide to have it repaired. However, you can charge the second damager only for the added cost of fixing the second scratch. In the following scenario, the second damager would have to pay more. The added damage from the second accident is that which causes the car to be in such a state that the average person would fix it despite the expense. In this case, the second person would have to pay the whole price of fixing the scratch he made, not just part of it. The rationale is the same as above: we compare the situation before and after the accident and require the damager to make up the difference.
Responsibly figuring out the car’s depreciation and whether fixing it is warranted calls for an experienced appraiser. Hiring one is probably expensive enough to encourage a compromise that all can live with as the best option for two honest people.