Q. Is it necessary to report the sale of an RV and pay taxes if we buy a replacement for the same price as the one sold or more? We are full-timers and consider this our personal residence.
A. For decades, when one sold a personal residence at a gain, you could avoid taxes only by buying a replacement residence for the same price or more. These rules went out the door many years ago. Today, the rules are simpler and no replacement is necessary. Here is a link to IRS Pub. 523 which explains the rules for selling a personal residence and reporting a gain.
I can't imagine anyone selling an RV today or even trading one in, at a gain. Generally speaking, selling a personal asset at a gain is a reportable transaction; selling a personal asset at a loss is never deductible. I don't think you have anything to be concerned about!