Just my guess but Roth's father brought Anna in the first timeline and I guess he told her the only way for her to go back is through the swan's grave where she came from, and her mother is still in her world so she had to go back, leaving Roth and her son behind, despite she love them so. In desperation, Roth and the son both attempt to bring Anna back several times with the help of that tutor snake lady, and I believe each time she messed up on purpose so she can be of use to Roth and stay by his side longer. Until the last attempt, she messed up so bad that it messed up with Anna's memories of the first timeline when she arrived with the boyfriend.
When she went back to her world the first timeline, she went back in time of before she met Roth, that's why shes much younger than she's supposed to. (=・ω・=)
if she's indeed the wife, i'm guessing that roth's father didn't only brought her to her original world but also back to the past before she goes to the swan's grave that's why anna doesn't have her memories and that's why her face doesn't change at all. the "him" ianna us talking about it the boyfriend for sure, because her father already dead and so her mother and since she probably already have a boyfriend before she comes to the swan's grave, she's like wanting to go back to him...
AURGHHHH I DUNNO!!!! spoil me peopleee!!
( T﹏T )