The above quotation is from the attorney.
All people think that there dog is different. All dogs are good until there is a problem. The word "dangerous" is from the attorney. It doesn't matter if rental is for a week, month, or year.
If you can find some place that does take a dog then take it.
There are many resources available including Strictly Rentals and Preferred Rentals. Meredith News, Laconia Sun, Laconia Evening News. And many on-line resources.
Years past there were more choices for cabin rentals. Sadly, the cabin has gone the way of the railroad. Still around but few and far between. Most weekly rentals are called homes now. The days of the seasonal cabin are waning.
New Hampshire relies greatly on the property tax. The cities, towns, and now the state. Property taxes are very high for waterfront - which makes seeking a cabin rental for a reasonable cost - few and far between presently.
And note - I do have a dog and I do think that my dog is different.