Sophie Turner Spotted with Daughter Hours After Suing Joe Jonas Over Custody

Sophie Turner is fighting hard to get her kids out of the United States and over to Europe ... but that's not stopping her from enjoying some QT with her kiddo stateside in the meantime.

Sophie was spotted out with the estranged couple's daughter, 3-year-old Willa, Thursday while running some errands in NYC. Both mom and tot had big smiles on their faces as they walked hand and hand with another female friend tagging along.

No signs of Joe, but that's not at all surprising given the drama that unfolded between the two earlier in the day.

Sophie sued Joe, claiming they had an agreement to raise their two daughters in the UK, where they believed they'd live a safer and healthier life. Sophie claims Joe's hidden the kids' passports, preventing her from taking them outside the U.S.

As for Joe's part, he sent us a lengthy statement explaining a Florida judge ruled neither parent is allowed to relocate their children outside of the United States while divorce proceedings continue.