In most states it's illegal to relocate many critters, and it's a bad idea. 'Kindness' it ain't! In a strange location, it won't know where things are, will have local competition, and may try to get home. And is now trap wise, and loves chickens.
Here in Michigan, for example, the trapped animal can be releases on the same property, or on private land within the same county, with landowner permission. ONLY!
We also have horses, and opossums carry a bad, often fatal parasite that affects them. And they will kill chickens at night. Not welcome here at our coop or barn!!!
All raptors are federally protected in the USA, so can't be injured or killed. Keeping chickens safe is the priority, with no harm coming to any hawks, eagles, or owls.
Mary