Peer one-on-one with someone who's not my peer?

I'm looking for some guidance on working with a particular individual. She (S) is high-performing direct who doesn't report to me, but is involved with a lot of my work, so I'm making a conscious effort to develop a relationship. When I was hired, I was told that I would have one direct report, and another (this is S) who reports to someone else but is a dotted line to me.

S is a hard worker and does great work even when she's asked to do things outside her job description, but she clearly doesn't like to. I have a poor relationship with her. On several occasions she has tried to set the agenda when we meet, and give me tasks. She has good ideas and I typically agree that the things she wants to do are things that should get done. But they are usually smaller tasks that bog me down and take up time that I need to focus on bigger projects, so I push back.

Our team doesn't have a very formal reporting structure and I'm not in the position to ask S's manager to officially get S for half her time (in which case I could set up a regular O3 with her as if she's my direct). I believe that part of her problem with me is that she feels is she is doing a lot of work that should be done by me or my direct. If I tried harder to communicate with her, I can improve the situation. This can probably be achieved with just a couple of conversations to clear the air, but since our work will continue to overlap, I thought setting up peer one-on-ones with her might be beneficial. But since she's not my peer, would this be a bad idea?