Other people already gave possible solutions, but one important thing to keep in mind when traveling, and one which trips many people, is this:
In some countries, you get driver’s insurance. This is the usual case in the US and the UK.
In some countries, we get car insurance. This is the case in Spain.
And no, it’s not the same thing; they’re orthogonal. The first type covers a driver for one or more vehicles; if you have that type, one of your options is to verify that your insurance will cover you for a rental vehicle.
The second type covers a vehicle for one or more drivers. Some packages do cover the payer for rentals, but it’s an “extra”, it’s not part of the basic package. If I had followed my British client’s instructions to reject rental coverage I would have been uncovered, because while my policy covers my car with any driver in any country, it does not cover me in any cars the policy does not list except when they are provided as a replacement while my car is in the shop. What is done if you take the rental company’s insurance is add you temporarily to their existing policy on that car.
Going from those generic “yous” above to the specific case, it is possible that the coverage you have as a secondary driver in your wife’s car can be extended to cover you for other cars, including a rental, or that they will write you a short-term policy for the trip. You might even be already covered. Since you already have a history with that specific company, it’s a good place to ask first.
Oh, and one thing that rental car companies are supposed to do but many do not, so check for it: the car should come with an “accident report form”. If you do have any kind of accident, you don’t need to call the cops unless there is a disagreement (which is unusual): each party fills up his copy of that document, everybody checks that yep, we’re all telling the same story, you hand over your copy to the agency along with the car, and that’s it. It is also pretty common for the accident to take place at a bad time, so people will trade contact info and agree on a place and time to meet and fill up the document: if it happens and the other person wants to do that, you of course have the right to refuse but it’s not that they’re trying to evade the situation or rip you off, it’s normal. The insurance companies take over from the moment the documents are handed over to them (someone will have to assess damages, but that should be done once the car is returned to the agency, you don’t have to be there).
This page has the general accidents report in PDF format. There is a different form if there are victims, but that case would involve cops.