My 2nd house is my parents' primary residence. If we sell it, can we ask a closing agent to make the check payable solely to my mother to avoid any capital gain tax?

My mother and I are both on the title of my second house.

I pay all the mortgage on the second house; my parents live there for free.

Although I cannot exclude the profit from my capital gain tax, if my mother files tax jointly, she can excluded up to $500,000, correct?  Then, as long as the profit falls under $500,000, can she claim 100% of the profit and me 0%?  If so, then all of our capital gain taxes would be $0, right?