Elroy,
Trach vs. sooner death is a serious decision that some people are happy with and others regret to the point of reversing it, with anguish for all involved. So please don't make it in haste just because someone's recommending it. It's still your wife's and your choice.
See the trach care required in person or on video, talk w/ the social worker, pulmnologist, etc. about your wife's likely quality/quantity of life with and without the trach. Look at posts by GilWest (gives care to a PALS w/ one), DianeH (has one), SantaJoe, Greybeard and others on the forums using the Search function. Those still living may chime in on this thread as well but have already contributed a wealth of information.
Facility vs. home -- that may hinge initially on reimbursement, complications from/tolerance of the procedure, etc. I suspect most people would prefer to stay at home if possible (is your home accessible?). There are financial strategies that you should discuss with someone more knowledgeable of your situation.
I know of no PALS receiving fully subsidized 24/7 long-term care, outside the Medicare quantity limits or via home health (people get some hours but not constant coverage reimbursed). That's another topic for a discharge planner or home health agency social worker, as States differ and I don't know your resources/ eligibility. But under pretty much any scenario, there are financial implications for a trach.
Best,
Laurie