Is there any problem with transferring title to two of our vehicles to our adult children?

Yes there is a problem. If they belong to a business, there are tax issues for the business to cope with.
Unless you have a million dollars put away for a nursing home, you'll need Medicaid to pay the bill. They will impose a penalty for gifting assets away. Sell the cars at fair market value.

Mopsygirl,
If the cars are in the name of a business, and if they work for the business, they can drive the cars.

It depends on whether you might need to apply for Medicaid within the next 5 years. Unless the children pay fair market value, this will be considered a gift.