We are retired living in our primary residence and paying a mortgage. We take the standard deduction. How would rent to cover the mortgage affect our tax’s?

Can you clarify what you mean by "rent to cover the mortgage"?  Are you asking about renting out part of your home?  Or the entire home while you are gone?  Or something else?

If you use the Standard Deduction and only use your RV for personal use, nothing is deductible.  If you Itemized your deductions, in some cases the RV loan interest could be deducted as Mortgage Interest as a second home.

@elpez , you should discuss this "new" plan with your financial adviser--- he/she would  know more details about your actual situation.

If the question is reduced to how your taxes would be impacted if you rented out all or part  ( say 50% for example ) of your  home, then:

(a) you still continue  using standard deduction ;

(b) You file a schedule-E reporting  -- gross  rental income, deduct  50% of your mortgage interest & property taxes,  take depreciation on 50% of depreciable basis of your prop.( Acquisition cost plus cost of all improvements over the years LESS cost of land at the time of acquisition ) , utilities etc. depends on your actual rental agreement.

(c) Note that while this may improve your cashflow situation, the depreciation ( accumulated over the rental period ) will increase your gain when the prop. is disposed off AND  the depreciation caused portion of the gain is taxed as ordinary income, the rest of the gain is capital gain and taxed as such.  The main residence gain exclusion gets murky here , depending on exacts facts and circumstances ( inclu. when sold  and if there are any step-ups ).

(d) Also this additional income may impact taxability of your SSA distribution.

Therefore the suggestion that you discuss this with your financial adviser ( for the long term ).  You can also try out as a "what-if" using desktop TurboTax using reasonable assumptions  for the short-term view.

Is there more one of us can do for you ?

consult with a tax advisor. There are many rules involved, including what's required for the RV to be considered a second home.