Taxis and Ubers are easy at LGA.

OP is headed for West 57th St. Should be absolutely no problem to head to the West Side at 125th St. and then down pretty much anything. Will completely avoid the entire "UN zone" which is not particularly bad at night anyway unless you want to park in front of the Cuban Mission or somesuch.

Take an Uber XL. It will accomodate the six of you and your bags. You will be in your hotel by 9:00 PM without your kids hating you.