Sophie Turner Spending Time with Her Kids After Night Out with Taylor Swift

Sophie Turner‘s sending the message that she can do both — have a fun night with Taylor Swift AND get in some QT with her kids — all amid her heated custody battle with Joe Jonas.

The “Game of Thrones” star was out with her kids Friday in Manhattan … pushing 3-year-old Willa and her 1-year-old little sis in a stroller.

Sophie’s low-key outing comes the day after her second dose of girls’ night with Taylor … remember, the ladies headed into NYC’s Hotel Barriére Fouquet Thursday night.

Of course, the backdrop to them hanging out is that Taylor briefly dated Joe back in 2008.

The women were like 2 peas in a pod Tuesday, hitting up Via Carota to grab some dinner together — of course, all while Sophie and Joe’s divorce really heats up.

As we reported, Sophie filed a lawsuit Thursday against Joe, claiming he’s unlawfully keeping their daughters in the U.S. instead of letting them go back to England with her … citing a child abduction law.

Joe’s denied any wrongdoing, and says Sophie’s actually the one violating a court order in Florida — where he filed his divorce docs — blocking both parents from relocating their kids.

We also got pics of Sophie and Joe grabbing lunch Monday in Manhattan. We were told there were no signs of drama that day … which, of course, changed with her lawsuit.