Hi Jenson, I am a little late in getting to this thread. First of all, I am sorry you had to go through this.
"With that plus the brutal killing or baby rabbits in mind, am I wrong to want the thing out of my shed?"
No, you're not wrong to want it out of your shed. And I, for one, can certainly understand what you are going through.
I work in a wildlife hospital, and when our wildlife patients are almost ready to be released, they have to spend some time outside in aviaries.
We have a problem in the park we are located in; it's not rats, but raccoons.
Everybody thinks they are so cute, and do not want to believe how destructive they can be. I have come into work too many times that I care to remember, to find that a raccoon found a hole in an aviary and feasted on our patients. 15 songbirds in one shot, at one time. Another time, tried to get a baby squirrel, but couldn't get it out through the hole it made, so we found the headless remains. I won't even go into any more.
So I truly know how you feel.
But poisoning is really not the answer. Rats don't just up & die right where you poison them. They crawl away and die slowly. Besides the inhumane factor, in the process, prey animals, not knowing any better, see an easy meal and eat poisoned animal, and in turn are poisoned themself. We regularly get in red-tailed hawks, great-horned owls, and screech owls that come in seizing and ultimately dies because rat poison goes "up the food chain". Just a few weeks ago, I got 2 red-tailed hawks from golf courses that put down rat poison. Both died within a few hours.
And I just wanted to point out to everybody: we are wildlife rehabilitators where I work. The reason a wildlife rehabilitator wouldn't help is not so much that it is vermin, but that is not what rehabbers do. Rehabbers are just people, who don't get paid a dime for what they do, who outside of their paying jobs, try to help injured wildlife (like poisoned red-tailed hawks). We spend our days,especially in baby season, feeding orphans around the clock. We are not trappers. For that, you would need to hire a wildlife removal person, and they can be costly.
I wish I had an answer for you; if I did, I could answer my own question. I feel for you, and for what you've been through.