Despite the rings both appear to wear in some photos, "They are not engaged and they are not married," says Twain's rep.
Photos show the group relaxing by Twain's lakefront cottage and Thiébaud, 39, jet skiing, horsing around with the kids – including her son Eja, 8, and his young daughter Johanna – and sharing some tender moments with Twain.
"She loves being back in Canada. That cottage is probably her favorite place in the world," says a source close to the singer.
The next few weeks promise to be busy ones for Twain. She'll guest judge on Idol's Chicago auditions, and she'll turn 44 on Aug. 28.
Included in the celebration plans: a "gift of thanks" to fans that Twain will post on her Web site, which will include a video travelogue documenting her life since her split with producer Robert "Mutt" Lange after his reported affair with her friend, Marie-Anne Thiébaud, a longtime manager of the couple's chateau in Switzerland.
A source close to Twain says she'll reference her relationship with Thiébaud in a personal letter that will accompany the video.
John K / Todd G / Splash News Online