Just wanted to add that my dual insurance (2nd plan premiums paid OOP) looks like it will pan out and save me $$. The coverage is about the same, but the billing people at my dentist's office tell me that since they are in network for my secondary insurance, I'll see write offs instead of balance billing. Fingers crossed that this works out!
Up until about two months ago, I worked for a dental insurance company, in claims. Basically, the advice others gave above is accurate. One thing though, If your insurance is through your work, that plan automatically becomes the primary plan for you, and your spouse's plan is secondary (unless your insurance company has REALLY odd coordination of benefits rules.)
So the way it normally works, your dentist sends the claim to your plan, gets a response, and then forwards that response and the claim to the secondary. The secondary will normally pay on what is left over.
Where it gets tricky is the IN network and OUT of network rules. Normally, the secondary pays as Out of network, again unless they have odd rules in their contract that allows them to pay as In-network. So, in spite of what your dentist tells you, there is a good chance it will be balance billing, unless he agrees to write off the difference. Many dentist office workers have NO IDEA how insurance works, so they just bill you whatever the insurance company tells them to.