Work in NY and Sold Land in PA

I have a vacation home not sold yet in PA, transferred into my name however, I would like to transfer it back to my retired parents as it is theirs. If sold in their name then they are likely paying less capital gains tax.

 

I work in NY and assume if it is kept in my name I would pay more in capital gains tax. Can anyone confirm if this is true? And for selling a home in PA, will I be paying only NY capital gains and not PA capital gains? How does this work? And if it happens to sell in my name, will capital losses from stocks be used to offset capital gains selling a home? What is the capital gains tax rate (for selling home)?