Mother refuses to take any medicine. Should I just stop giving it?

Yes, stop giving it. What are you going to do otherwise? Shove it down her throat?

That said, and as AndSoItGoes already wrote, it sounds like you are the only one who can make decisions for your mother that would end in her having a good death rather than the horrors that are currently unfolding, which will lead to a gruesome death.

I don't know how to get hospice for her without going to the hospital. But maybe someone else here does.

Is there really no palliative treatment that could manage pain and discomfort from a death caused by sepsis (assuming the UTI progressed to sepsis)? Mom is being kept alive, through modern medicine, in a state that her earlier self (her "real" self, in my view, but the philosophers can have their "then-self"/"now-self" arguments) would have regarded with absolute horror. In the pre-antibiotic era, this would have been a potential exit route. 

What is the goal we are pursuing here? What is the "good death", versus stroke or sepsis, that we're hoping for?

This is a real question. I'm trying to understand. Is the idea to treat the things that would cause immediate harm and suffering (worsening of UTI, stroke from high bp) in the hope that there will be a peaceful death-while-sleeping at some later date?

Now that modern medicine can treat so many things that used to kill, don't we need to think this through? By treating, we've already decided not to leave matters to a higher power or nature. So aren't we responsible for ensuring that we're not doing actual harm by dragging out the dying process?

To the extent that we have any respect left for mom's personhood, don't we have to honor her refusal of the medications?

Again, I don't know. These are not rhetorical questions. These are questions I'm wrestling with.

I do know that if my own mother developed dementia and refused blood pressure medication, I would honor that refusal. What would simplify the matter for me is that she has HATED blood pressure medication all along. 

The UTI stuff I understand less well. My mom's culture came back positive for UTI the last time she was hospitalized but the doctor said they don't treat when patients (he perhaps meant patients my mom's age) are asymptomatic.

My own advance directive, which I hope is honored, says to administer absolutely no life-prolonging treatment if I reach the state described by the OP (though of course it expresses a hope for efforts to alleviate my suffering through the dying process).

I would call 911 and tell them you think she has sepsis and she needs to go to the ER. Then I wouldn’t take her home any more. No one needs an adult size person urinating all over the floor.

She sounds like she needs 24 hour care and you are unable to provide that (understandably). Don’t let the hospital discharge her home.

Or call APS and get her evaluated and placed, but it sounds to me like she very well may have sepsis.

Is it a low grade antibiotic for chronic infection prevention?

She needs to at least take the antibiotic for the UTI. Once she is cleared of that infection, her behavior may improve since that's what a UTI can do to a senior. An untreated UTI can turn into sepsis, which is life-threatening. If you can't get her to take the meds, you may need to call 911 and tell them she is delusional/out of control and maybe the hospital can get the meds into her, but be aware she may pull out the IV. That's what my 100-yr old Aunt did after she went to rehab for a broken hip. Wouldn't keep in the IV for fluids, wouldn't stay in bed. She passed while in rehab.

You should call the pharmacy to find out if the antibiotic (pill) can be split in half or crushed so that you can disguise it in some other food. Or see if there's a liquid form of it. In the end you can only do what she allows. One of the trickiest situations is trying to care for someone with advanced dementia who is still mobile and strong. She may need meds for agitation and this may bring her to a state where she might actually take the meds.

I'm so sorry you're in such a distressing situation. You are doing your best. Also take care of yourself.

If your mother is in “…the last stage of dementia….” she is most likely incapable of actually thinking that anything is “funny” or “not funny”, so while she may “laugh”, that behavior may be more reflex than thinking.

Defecating/urinating/ on the floor to relieve herself doesn’t really sound like a very positive situation for either of you.

If you feel able to manage her care needs in terms of what is “wrong” in your mother’s care while continuing to accept her current toileting habits, and if you’ve had input and hopefully suggestions from any medical specialist(s) who are seeing her, how do you feel about assuming that responsibility on her behalf ?

Get a medical opinion from someone who knows her, then decide, based on that opinion, what she and you should be doing next.

Be sure you’re including some relief for yourself, every day, from this caregiving schedule.

Mother needs 24/7 aides or a facility. The UTI is making the dementia worse,

“antibiotic for UTI. Is it wrong to let the medicine go?”

Yes it’s wrong. She has dementia. She doesn’t realize the consequences of not treating UTI. Do YOU know the consequences? Bad UTI can lead to sepsis: a horrible, painful way to die.

You don’t have dementia. You decide. Not her.

“uses the floor all over the house”

Why are you letting her live like this? What would you want if the roles were reversed? You’re family. She won’t listen to you. She might listen to a hired in-home caregiver. She’ll listen also to caregivers in a facility.

“uses the floor all over the house”

Letting her live like this, sounds a lot like elder abuse/negligence.