Respite care for someone with a colostomy?

Is your dad on Hospice? If so Medicare does provide for Respite for Hospice patients.
You can contact an Assisted Living or Skilled Nursing facility and ask if they will take him for 3 days, 5, days however long you expect to be gone.
Dad pays for respite not you.
If dad is a Veteran the VA may also provide some help. (and depending on when and where he served that could truly impact the amount of help you can get. If he is a Veteran contact your local Veterans Assistance Commission they will provide the information and the service is free.

We had a similar situation in seeking Board and Care for my MIL following a hospitalization. None of the B&C homes were prepared for, or licensed, or whatever for an iliostomy. When we mentioned this at the hospital the suggested we talk to the ostomy specialists in Wound Care. We did that and found that they would go to the B&C home to teach them how to care for the ostomy divice as needed. Although MIL did not have dementia and was accustomed to handling her own device, we did need B&C to know what to do, and how often it needed to be done. The B&C was open to that and an ostomy specialist went there and had a session with them prior to MIL moving in. Then the specialist visited a couple more times to see how things were going.

So, maybe talk to your insurance provider within Medicare to see if they have ideas, or a hospital social worker, or any support groups for ostomy wearers.

It is your father who needs to be able to afford care, not you.

Is his delerium being managed by a geriatric psychiatrist?

Have you gotten him qualified for Medicaid?

You might try contacting the company where you get his ostomy supplies, and ask to speak with their ostomy nurse. She may be able to give you some ideas. Also, there are ostomy support groups, they too may have some ideas. My mother has an iliostomy and Alzheimer's. It's such a wicked combination to deal with. I am blessed that my parents elected to move to a graduated care facility when their doctor told them it was time. But until mom's AD advanced to where she needed memory care, helping her deal with the ostomy (no nursing care for that in independent living, nor assisted living) was a daily struggle. During that time I found I got my best tips from ostomy nurses. Sadly, there just isn't much knowledge on dealing with ostomies and dementias as this seems to be the first large scale generation of ostomy patients to have lived long enough to develop dementias. My heart goes out to you. Also, the suggestions to get your dad on medicaid are good suggestions. This too can be a stressful process, and you'll want to get some help, probably from the area agency on aging. It sounds cold to say it is your dad's responsibility to pay but it is true that it is his finances that determine what help you can get. You cannot be held financially responsible for his expenses the way you can for your child's. It is important to keep his finances separate from your own. Your role, aside from loving him, is to advocate, case manage, and care coordinate. Not something any of us are generally prepared for, but support groups help. You will remain in my thoughts.

Call his doctors office. Quite often doctors are invested in or have ties to certain facilities. Maybe able to find you a bed for the days you will be gone. More than likely private pay, but if dad living with you his income should be able to cover a few vacation weeks a year. Dr may have contacts with nursing services as well. You would probably do best to do a trial run with someone first to see how they manage the care your dad needs based on their own nursing experience. There are quite a few older people who have retired from FT employment, but continue to do sitting/caring services.

If doctor is of no help, call your area Aging Services. Or check online to see if they advertise short term facility care. Taking him out of the house would be my Plan B. Plan A would be to bring someone in to his familiar territory so as not to create confusion for him

Going with Grandma1954's suggestion,  the VA has expanded its caregiving support.    I haven't followed all the changes, but I do recall reading something about respite care.

https://www.va.gov/GERIATRICS/pages/Respite_Care.asp

I don't know how COVID affects this program though.  

Your post reminded me of one of the stories in a Chicken Soup series:   Tough Times, Tough People.  The situation was different; this was during the 2008 financial crisis.   A couple chose an inexpensive alternate to a vacation, stayed home, and explored their own area, learning more about it as well as meeting people, and enjoying themselves w/o having the leave the area.

I found some very long, huge links,  but you could get more just by searching on "Sally Friedman, In Praise of the Staycation".  One adaptation that could be made is that either you or your husband spend some time away from the home, while the others stay there to help with your father.  

That way each person gets a small vacation, but the family is still available to help him.   Rotating vacations also gives your family something to look forward to. 

Can you pitch a tent in your back yard, and pretend to be camping out...and away?  

Another inspirational story is by Deanna Lowery, "Better than a Tent".   Neither are directly related to home care, but they reflect how people in very difficult situations find ways to cope.

And it's not my intent to trivialize your frustration; I can certainly understand it. I'm just applying some techniques I learned in the Alz. Assn. "Creating Confident Caregivers" educational series. One very helpful technique was kind of a geometric equation:  A=B but A can also = 1/2 B +1/2 C, which is why I suggested taking different relief times.

Have you tried hospice care. Or put in hospital or nursing home for respite care. You do need to take care of yourself And your family in order to care for your father. I had hospice care come in 2 or 3 times a week. They helped with putting him in hospital so I could rest I slept for almost a week I needed that in order to take care of him when he came home .it was a blessing . He passed at home which was what he wanted. Take care and God bless.
I am shocked at the home care you tried. Try hospice care they do come to the home.

Some nursing homes will provide respite care. Check local ones. Their nurses are LPNs and can handle ostomy bags as well as medications.

Respite care can cause problems. Changes in routine can make a person with dementia go crazy, and start pulling things out like his ostomy bag. Depending on his level of function, they can start kicking staff. They can also stop eating.
And whatever contagious disease is going around in a nursing facility like nursing home, it spreads around. Scabies, lice, COVID, are among a few things he can get.

Unfortunately it is true most caregiver services will not handle certain medical conditions, particularly if they require constant attention. Your only alternative is to have a family or friend that knows how to handle the patient’s situation. Otherwise you can look for a Nursing Home that will provide the services as a temporary “respite” resident, but it will be expensive, and not covered by Medicare.