Makes sense from the point of view of the welfare of the child; strictly speaking, it is not unprededented for an American President to maintain a residence in New York ...
Following his April 1789 inauguration, President George Washington occupied two executive mansions in New York City: the Samuel Osgood House at 3 Cherry Street (April 1789 – February 1790), and the Alexander Macomb House at 39–41 Broadway (February–August 1790).
Nice bit of history there. I should bookmark that.
I believe that Teddy Roosevelt also kept a home in NYC during his entire term.