Take the Reins — Siobhan Muir

Social change is normal for a senator's daughter, but affecting gender politics in centaurs wasn't on Bethany's agenda.
All Bethany Stanton needed was time away to think. She never imagined a walk with her horse might lead her so far from home. When she steps through a rift between worlds at an old archaeological site, she realizes she has bigger problems than marriage to the man of her nightmares. Like a herd of centaurs with distressing views on gender equality and “mythical” humans.
As part of the Supernatural Anomalies Investigative Field Unit, Major Stephen “Mack” McMacken has seen and done more weird stuff than written in a science fiction novel. When called in to track down a U.S. Senator's missing daughter, Mack figures it's more a case of runaway rich girl than supernatural mystery. Until his team finds the portal and he's nearly torched by a dying phoenix.
In a world ruled by mythical beasts, Mack and Bethany find themselves on trial for endangering the centaur village. With the only escape route they know gone, working together to establish their innocence might prove easier than avoiding seductive Sirens and ravenous native beasts.
And then there's the not-so-simple matter of finding a way back home…