If your Havahart trap isn't getting him/her it may be because the trap needs some adjustment, or it may just be that it's the wrong size. They come in three common sizes in my area, and it takes some experience to guess which will work best for a given animal. It is NOT necessarily sufficent that the animal "can fit" into the one.

If this 'coon has been trapped before, it's quite possible it's figured out how to open the trap, and another method may be necessary - or a different style of trap.

An animal control agent, or someone who fancies himself (with credible justification) a great "critter rassler" would probably attempt a "noose stick" to just get a rope around his neck and drag him into a sack. I do not recommend that you try this yourself since there's considerable "technique" involved that isn't all that easy to learn in a one-shot givitatry attempt, and considerable strength may be needed once (if) he's "noosed. 'Coons can be quite dangerous in close quarters, especially when cornered or snared.

If you don't have an official animal control agent handy, ask at the local hardware or other "gathering place" (or at a gun shop if there is one) if they can suggest someone with "experience." (And get a credible story about the nature of the experience if you don't know the one(s) suggested.)

Your 'coon is unlikely to do any major damage if left alone while you look for a solution, unless you have food stored where he might try to get into it. If he's knocking things over he's probably chasing the rats.

If it absolutely comes down to destroying the animal, you don't need a 12 gage. A .22 short would be about the minimum appropriate, at short range, and most .22 rifles (and any .22 revolver) can use "shorts.' (Rifles may require loading single-shot for the shorts.) Someone in your neck-o-the-woods will have one.

John