I believe you are looking for the novel "Summerland"
Items that match:
- Publication date: 2002
- Baseball is the central theme
- Travel through a fantasy universe collecting players
- Saving the world from Coyote (Trickster from Native American legends)
- Meet baseball legends along the way
Item that doesn't match
- Protagonist is male, but one of his traveling friends is female
Summary from wikipedia, which matches most of the details of your recollection.
The story begins on a small island off the coast of Washington called Clam Island. The central character, Ethan Feld, is on one of the island's baseball teams despite being terrible at the game. He encounters a gracious werefox, Cutbelly, who explains the Lodgepole, a giant tree connecting all worlds, to the ignorant Ethan. Cutbelly explains that Coyote is planning to destroy the Lodgepole, an event called "Ragged Rock", by destroying Murmury Well. He takes Ethan to the Summerlands where they meet small Indian-looking people called ferishers. Coyote captures Ethan's father and forces him to create another batch of 'picofiber' to form the hose with which he is going to poison Murmury Well. Ethan enters the Summerlands with fellow baseball team members Thor and Jennifer T. Rideout, in pursuit of his father and to prevent Ragged Rock. On their travels through the Summerlands, the three assemble a baseball team and play their way across the land, meeting players from legend and literature, and a couple from their own world.