Gosh!
It's too bad your DH won't back you up on this and take a stand. I think it's his position to do so since this is his kin.
However,
you are paying PART of the rent. As such, I think that if he won't do it, I would (if I were you) write a letter, laying down some much needed ground rules and boundaries. Ground rules/boundaries about unsolicited visits and/or any other situations that are (essentially) NONE of her business! That means, both to your house and/or chicken coop.
You should NOT have to put up a lock. That's crazy! :|
(I mean, for crying out loud...YOU ARE PAYING RENT!)
Sadly, this is the worse case scenario but sometimes you have to be RUDE with people or they just don't/won't get it!
I know she means well and all that jazz but, it's obviously creating a lot of stress for/to you and probably between you and DH.
-Someone has to take that stand or you will have to cave in to her and butcher your birds and move.
-Or you can, just give her the benefit of the doubt and write that letter...and give it to her or drop it in her mailbox. Assume...she does not know this type of etiquette.
Now, I'll get off my soapbox.
Good luck and I hope, I hope, I hope...you don't have to butcher your chickens as a last resort. :aww
I just don't give people that much power over me...
Peace-
Pedro