Congratulations on your new driver! I think you might be working under some incorrect assumptions. Here are your questions and my take, in the order you asked them:
Would it be better to sell the Yukon and buy a new vehicle, or is it better for insurance if we buy a used vehicle?
A Yukon is a big, heavy vehicle. It’s also one of the cheapest to insure for injury and collision claims. Not so for theft, however. That being said, yours is pretty old already (2003) so getting a different used car doesn’t make a lot of sense, unless you are buying something small and very cheap to fix. Even then, such a car would cost more on the injury coverage side and might not save you much anyway. You seem to be in a good spot already with the Yukon.
The Yukon has an actual cash value between $5,000 and $10,000 (you’ll need to look up your specific package, extras, mileage etc. on Kelly Blue Book or NADA to get an accurate assessment of the value). If you don’t have that kind of cash lying around, you should keep full coverage on the Yukon.
Or, you could sell it and buy an affordable used car for around $5,000 or so and keep the rest in the bank in case the worst happens. Then you can scrap the collision coverage, saving a few hundred per year. You should look at every car you own in this light to see how much you can save.
As far as buying a new car, that sounds like a bad move insurance-wise. Newer cars are more expensive to insure as a rule, and the Yukon has a good rating profile. If your going to sell anything to find cheaper rates, make it the Jetta. It has the highest value and the greatest repair costs of the three.
Should we keep the Yukon and add another vehicle?
This part of your question really has me perplexed. I have never heard of four cars being cheaper to insure than three. There must be some part of that equation I am missing. Were there three drivers and four cars? If one of the cars is an extra and is rarely driven, then it would make sense to pay less because the multi-car discount might be enough to offset the cost of the extra car. Even then, however, it seems incredible that a fourth car would be cheap enough to insure that discounts would make the policy cheaper. It would not be in the insurance company’s best interest to take on that fourth car.
Not knowing where you got that information, it’s hard for me to figure out how the person came to the conclusion it would be cheaper. If it was an agent, he or she probably meant a cheaper rate. That would mean you paid less for each dollar of coverage, but the total coverage overall would have to cost more. I can’t imagine a scenario in which it wouldn’t.
Adding another vehicle is VERY likely to cost more overall. You could look at a used car for your new driver to keep insurance costs down, but it will probably be cheaper for the two to share a car. The only way to know which option is best is to get insurance quotes on each scenario. Every insurance company calculates things differently, so you never know until you get the quotes and compare them.
Also, can we choose which vehicle the 16 year old is put on?
Insurance companies rate the costliest car with the costliest driver. You rarely have the opportunity to pick and choose. Too many families haven given false information about which person drove which car in order to get artificially lower rates. For that reason, insurance companies assume the worst driver will drive the car that costs the most to insure.
I hope I’ve steered you in the right direction. If it was me, I’d sell the Jetta, get a dependable used car with no loan and put the extra cash in the bank to cover a potential total loss. I’d do the same with the Yukon. You’re probably better off holding onto the Elantra since its cheap to fix and replace. Then, the kids can share a car and your insurance will probably be cheaper than before you added your new driver.