I hope you have known her longer than since August. If not, this is a really quick romance. She needs to worry about the custody of her children; their father has rights too and may object to them being relocated permanently to the US.

Just because she has a trainee job at the university means nothing in obtaining a full time, regular position. She must wait for work authorization but that is minor compared to getting a "real" university job where it is far cheaper for a university to hire a post doc than a faculty or research staff member.

If she marries you, she will have immigrant intent and her tourist visa is worthless.