Since vinyl is a lower-risk building material than cedar, it is more likely that your homeowners premium would reduce rather than increase. For more information, call your insurance company’s customer service line to see if they will adjust premiums for the building change.
Typically, an insurer would prefer to handle any and all damage incurred as to avoid any unnecessary future risks of property damage or bodily injury caused by the damaged structure. This is a claims-related question that would be uniquely handled by the claims department of your insurance provider.
Your son would not need to be listed in any way on the policy unless he is a part-owner. Any payouts from insurance would go to the lender and homeowner(s), so having him on there would not do anything for him.
If it was not disclosed to your insurer at the time of finalizing your policy that you're running a business out of your home, it is within the company's right to void it. While you likely won't need a home daycare endorsement if you already have separate liability insurance, every potential home insurance company will want to know that your home is also a place of business.
Similar to how individual companies have different underwriting methods to determine rates, every insurer figures their replacement cost for a home differently. Some use tax records, mortgage info, average property values, and other data.
The best course of action would be to call that insurance company and request all paperwork associated with that claim. It should show as a zero dollar payout, which you could show to other companies to dispute the claim.