50 CFR 21.29...blah blah blah. I can't properly cite these things, their hierarchy in the regs makes my eyes bleed. Anyway, this is in there somewhere.
(2) Falconry facilities on property you do not own —(i) Your falconry facilities may be on property owned by another person where you reside, or at a different location. Regardless of location, the facilities must meet the standards in paragraph (d)(1) of this section and those of the State, tribe, or territory from which you have a falconry permit.
(ii) You must submit to your State, tribal, or territorial agency that regulates falconry a signed and dated statement showing that you agree that the falconry facilities and raptors may be inspected without advance notice by State, tribal (if applicable), or territorial authorities at any reasonable time of day, but you must be present. If your facilities are not on property that you own, you must submit a signed and dated statement showing that the property owner agrees that the falconry facilities and raptors may be inspected by State, tribal (if applicable), or territorial authorities at any reasonable time of day in the presence of the property owner; except that the authorities may not enter the facilities or disturb the raptors unless you are present.I could be wrong on this, not sure about your specific state regs, but you can have your facilities at another property as long as you have written permission from the property owner/leaser.

If that doesn't work, As Aaron said, Kestrels are easy to house inside, mine lives in my living room on a perch. And he is the 6th one I have housed this way. In fact, just about everyone I know agree that you SHOULD keep your kestrel inside. Way safer and better for a myriad of reasons.

Whichever you decide, good luck, welcome to the community!