“Research outreach”
Outreach is an institution's work to engage or inform the public or local community. Research outreach here means researchers sharing the interest of science with children. The job Tina's mother sent is mainly teaching rather than research, explaining it's less research and more teaching.
“If Grandma hadn't gotten sick, I wouldn't even be thinking about it.”
This mixed conditional connects an unreal alternative past to an unreal present situation. If + had + past participle imagines Grandma not becoming ill, while would + be -ing describes what Tina would be thinking now. Without that past event, she would not even be considering the job.
“That's why I'm torn.”
Be torn means to feel pulled between two valued alternatives. The pattern I'm torn between A and B. is common. Tina is divided between a job near her mother and grandmother and her current life with Frank and the team.