Gold, Gangs, and Glory (#3 in The Worlds of Ryn Wilkie)

Jack Varga is falling for Ryn Wilkie, a young surgeon who can jump to parallel worlds. Jack would like to have a serious relationship with her, but he might be too much in awe for her to take him seriously. He has his own secret though.

Ryn's starting a patchwork surgical fellowship while continuing to try to help the people of Cearth, an Earth with the technological level of our late 1800s. She wants to improve the plight of women on that world - but is realizing that raising everyone's standard of living may do more for women than just trying to get them equal rights.

Ryn’s brother continues to have financial trouble. She gives him some gold as well as financial advice, but he gets in trouble with a gang over the gold. Now the gang's after Ryn!

Oh, and that other parallel Earth she discovered? The one that doesn't seem to have any humans? It still has some animal species that've gone extinct here on Earth...