Well, first off, your insurance probably won't cover a visit to another dentist for a second opinion. Cavities are generally found during their 6 month check up, which is usually covered to some (if not all) extent, and then the following appointments for fillings are covered to a lesser degree. You should check with your plan.
If I were you, I would have the cavities taken care of, and also have your child's teeth sealed. It goes a long way to preventing cavities! If you don't have them taken care of, they will get worse and cause your child pain, if not the loss of his teeth. My niece recently had ALL of her front teeth pulled due to poor decision making on her mother's part about her cavities. Now she is 6 yrs. old, in school, with no teeth!
As far as your twins go, my twin boys are 15mos. and have already been to the dentist. They each have 8 teeth and are beginning to get their molars. They had a preliminary tooth and gum health appointment in which the dentist checked their gum health and the health of their current teeth, and gave us some great pointers about tooth and gum care for them to continue to have healthy teeth. This was completely covered by our dental plan, as it is considered a 6 month check up. We were advised that the first dental visit should be made 6 months after the first tooth is cut, which is what we did. Luckily, it lined up with the time that my daughter and I were due for ours, so we all went at the same time!
I have no experience with having laser dentistry done, though my husband is going to have his teeth done that way, as he hasn't been to the dentist in at least 12 years, and we were told that it would be less painful for him.
Good luck to you!