Should I stay or move on?

I am in a relationship with a woman who has been married 3 times. She constantly is bringing up her ex's in our conversations. She also tries to push the foods and customs of her has husband on me. I am Mexican and her last husband was Syrian. I tried telling her that I do not appreciate her pushing his food on me or his customs. I am ME.She tells me that her children like his food and I think that is fine and all but don't push it on me. I don't push my customs and foods on them. I really want our relationship to work but she is making it hard by doing this. Should I walk away? Thanks for the help.