How do they handle doctor's appointments in skilled nursing facility?

My dad was in a SNF for better part of a year last year and they used an in-house doctor the entire time. His primary care doctor was essentially 'put on hold'. They brought in mobile optometrist and dentist too. He never left for any services. When it came time to move him to memory care, he went to his primary doctor within 3 days of discharge (something about Medicare?).

My brother-in-law is in a SNF, and they use their in-house Dr. or PA/nurse practitioner for everyday things that you'd go to your primary care dr. for. He's taken out by them for needed specialist visits, e.g. neurologist, gastroenterologist, dentist.

IF you are able to safely take him to doctor appointments you can continue to do so.
Facilities do have an "in house" doctor that is called in and orders meds, may see someone if needed. (I suspect most of it is just chart review, signatures that need to be done. I think in many cases the Nurse will order a med after consulting with the doctor, for something standard, and the doctor signs off when he/she comes in.) And the house Dr. would renew any continuing meds. Also they would order any lab work that needs to be done.
If a resident is seeing a specialist the facility would arrange transport if the family can not safely take them.
Anything out of the ordinary the facility will call 911 for transport to the local ER

Honestly each nursing home (NH) and state regs are somewhat different. And it also somewhat depends on if the NH is also Medicare/Medicaid qualified or not; as well as what the facility type is (Rehab hospital only, skilled nursing facility (SNF), long term care type) as the NH will have many other federal regs that also apply. And also, somewhat depends on who is paying (self/private, private insurance, Medicare, Medicaid or some combo.)

The better NH facilities generally are both Medicare and Medicaid qualified as those federal rules then require many things (RN on staff all the time, "care plan meetings," COVID-related data reporting, qualify of care requirements and reporting, discharge rules, on and on). Most higher-quality NH facilities will have physicians on contract -- or on staff -- of differing specialities that are right there at the NH throughout the work week and on call weekends and evenings; making doctor visits simple (they just come to the room and handle it for the most part there). Most also have other providers on staff right there: dietitians, physical therapists, social workers/mental health providers; and visiting providers like podiatrists, audiologists, and dentists. Most quality NH will ask you to pick a "primary physician" from their list to be your LO's primary doctor moving forward while at the NH (even it if is a temporary stay) to coordinate all the care right there at the facility. Worth looking for a facility which has a variety of board certified physicians on contract or staff right there and even better if most/many of those MDs are board certified in geriatrics; but if not give these providers generally work only in the NH facility, they are much more experienced in geriatric-related care than other physicians in regular practice outside of a NH setting.

When something specific is needed -- such as a specialists not on staff/contract or medical tests/procedures that cannot be done at the NH -- the care team at the NH should schedule and coordinate those limited outside doctor visits. Most NH want to limit the outside visits of any kind -- doctor or otherwise -- because of COVID now. They will also coordinate medical transport as needed. NH have contracting pharmacies so any prescriptions are handled through the NH, don't bring any prescription or other medications (including supplements) to your LO at the NH.

Giving your primary physician at the NH and their care team there the role to coordinate care, make any outside doctor visits is the way to go as those folks at the NH are on point for your LO's care while there. As needed/if needed, the primary physician picked to care for you LO at the nursing home -- and the NH's care team -- will order and coordinate care needs with any health care providers outside of the facility.

If your loved one is difficult about this, let the the NH care team explain how things will be done. Also, worth getting any paperwork done before entering, such as a durable power of attorney (POA) so someone else can handle things -- financial or otherwise -- as needed. Not that you need to take over immediately, but to be prepared if and when you or other family members need to step in more. Ditto, for executing an Advanced Directive that spells out your LO's wishes for medical decisions if he cannot do it as well as naming a "Health Agent" who is the primary person (family member) the NH facility needs to inform if/when there is a "change in status" and the person the facility needs to communicate/coordinate with (family) on behalf of your LO.

There is usually an in house doctor that will care for all residents.

I do not have an answer but my father sounds like yours. He needs to be in a SNF but he won't go. He sent home health away and has to have my stepmother's children take off to take him to the doctor, which I feel incredibly guilty about. But he moved when he got remarried after my mother died against my wishes. And my brother moved out of state right after my dad's diagnosis. We are just waiting on the next fall as well.
I appreciate you asking this question, as I have wondered about the Dr. appointments as well.

My Mom was fairly healthy when she entered the SNF. Her Dementia is what got her in, the need for 24/7 care and Medicaid. I was given 3 doctor's to chose from. I picked Moms PCPs backup. The dentist and Optometrist were brought in.

I think it depends on the SNF and if your on Medicaid. Moms PCP did not take Medicaid so I had to choose from the Drs affilated with the facility.

Nursing homes most of the time have the residents seeing their doctor and not the patient's own unless it's for a specialty.
The facility is supposed to manage transport and even send an aide with the person who has the appointment. Most of them just send the person to their doctor in an ambulance then leave it to the EMT's to escort them and stay with them during the appointment.
It is up to the nursing home to make sure the resident gets to the doctor though.

Ideally, you use the in-house doctor who comes to the facility. Not only is it more convenient, that's going to be a doctor specifically skilled in geriatrics (though not necessarily a geriatrician -- they're few and far between).

This is also a good time to scale back on the specialists. The PCP at the facility should be able to coordinate care and prescriptions without endless office visits to orthopedists, pulmonologists, and cardiologists. It's time to refocus on quality of life rather than trying to cure every ailment that in the end is incurable.

I use my own PCP in skilled nursing and my surgeon. My PCP comes to the nursing home. Visits to his office and the surgeon’s office my husband or my nursing home arrange my ambulance transport. The first time I was in for rehab, the nursing home doctor changed my medications with bad results. This time I prearranged to have all my medical care done by my own doctor. I am a diabetic and have to have 4 blood sugar checks a day. Then my insulin is adjusted accordingly. The nursing home doctor messed my insulin up the first time.