How would you conjugate this? I'm thinking it's: Me quedo, te quedas, etc. bu not 100% sure.
Kyle - exactly right. The infinifive of such verbs is always shown with -se on the end as here. Furthermore, if you have a construction that uses the infinitive, you can tag appropriate pronoun on eg we want to stay - queremos quedarnos, as well as putting it before conjugated verb.
Sooo, she doesn't want herself to stay here. And if she doesn't want you to stay here, would that be Ella no quiere quedarte aqui? Sorry, I'm just rather lost on this right now.
It would require the present subjunctive. Ella no quiere que tú te quedes aquí. (She does not want that you stay here.)
Reflexives seem to be pretty sketchy in consistency. This literally translates as "She doesn't want to keep herself here". If we stick with "She doesn't want to stay here" it should be "Ella no quiere quedar aqui".