I am so frustrated because I try to be patient and caring with my 85 yr old MIL with dementia, but I'm failing.

It's not too soon! It is REALLY not too soon. For any of you! The time to place her is NOW! For your quality of life and hers.
Think of it like this - if she had a fracture you would take her to the hospital to get it fixed. If she had an infection you would give her the medications she needed to treat it. If she was an insulin dependent diabetic you would give her insulin. These are medical conditions that require specialty care to treat. Dementia is no different. It is a medical condition that requires specialty care, in this case, placement. Placement in a environment that allows her to be the person her medical condition is creating her to be. Her condition takes a TEAM of people around the clock to care for her properly. I honestly believe it is the kindest, most loving and unselfish thing to do for her. You can't be what she needs, no matter how hard you try. It simply isn't possible. It's not a "fault" or a "failure", it is a fact! NO one person (certainly not her son and daughter-in-law) can provide her the care she needs. Be kind to yourself and your husband - and most of all to your MIL! Best wishes!

Patience and dementia- can the two co-exist? You're becoming impatient with your MIL asking the same repetitive questions, and with her accusing you of not caring, and with your DH's lack of understanding. And although you haven't specifically mentioned his emotions, other than him misconstruing your anger as being directed at him, I'm sure his patience are also wearing thin.

As a previous caregiver for my wife, I've come to classify our emotional states as annoying, frustrating, anger, and resentful. I got to stage 3, anger, before realizing I couldn't do this anymore. That was after trying home care and day care. You and your DH already agree to placing his mom in a care facility eventually. I can assure you it's not too soon. It may be too early for MC but not for ALF. Planning to place her in the near future precludes you from advancing to the anger and resentful stages of caregiving.

And what's with the Catholic guilt? Where does that come from? My parish priest's mother had Alzheimer's and he eventually placed her in MC. Many people say that God doesn't give us more than we can handle. When it does become more than we can handle, it's time for a way out. That way out is a care facility. Your feeling of guilt, which, by the way is misplaced, shouldn't prevent you from doing the right thing for your, your husband's and your MIL's well being. Does your culture and upbringing require you to care for your family regardless of the situation; regardless of it's effect on your sanity, your health, your marriage? I don't think so. And from the sounds of it, it's time to start looking. So, considering where your MIL is in her level of care, and where you and DH are at your emotional stages, can patience and dementia co-exist? I don't think so.

Turn your thought around a bit.
YOU are not "failing" it is your Mother in Law that has a "failing" brain.
You know you are doing what you can to help her.
She just can not remember that you are doing all that you do.
When you want to yell..walk out of the room.
or, and this threw my Husband off for a while.
I laughed. When he was insisting that he wanted to do something and I did not want him to do whatever it was...I just laughed at the situation. He started to laugh and it was easier to redirect him to something else.
Anyone that says that they can be a caregiver and NOT get angry and yell is lying. So you are not alone. Walk away, walk out of the room if you can. If you can't leave then breathe, count to 10 or 20 or higher. If you can wear ear buds or head phones it might help some of the time.
Hang in there.

Thank you all for the encouraging words and advice. My husband and I are planning to eventually place MIL in MC. He has already said let's place her, but weirdly, I'm the one that thinks it's too soon. It might be my culture and upbringing, or maybe Catholic guilt lol. She is still mostly continent and knows us most of the time. I would get someone to help me, but the virus is raging in California, so I'm reluctant. When my husband is home I can leave, but again because of the virus I can't go anywhere but the grocery store anyway. When she came to live with us we were already in the middle of stay at home orders. I keep telling myself that I couldn't go anywhere even if she wasn't here. In that way the virus makes the decision to care for her at home a bit easier to handle. Taking care of an elderly parent is always difficult, but I'm realizing that the dementia really makes a difficult situation more challenging.

Perhaps take a long weekend away from her and leave DH in charge?

I imagine he'd get a clue pretty darn fast when he has to be in charge for more than a couple of hours.

Dh spent a night, maybe 3 times, at his father's when he was sick. DH didn't ever get up at night, he simply slept in the spare room and then took dad to the coffee shop in the am. Yet he'd come home completely exhausted and have to sleep for 2 days afterwards.

Giving your DH a chance to do what you do for a few days would probably help him to come to the conclusion that a NH may be a better fit for his mom--and save you a lot of anxiety and grief.

YOU are not failing, your MIL is, and it's NOT YOUR FAULT. Very few people can navigate the waters of FT CG without losing it now and then.

As you are discovering, caring for someone with any kind of mental decline, is beyond hard, and wears your patience thin quickly. You are doing the best you can, and that's all any of us can do. Yes, you will lose your patience every now and again, and yes, you will holler at the person every now and again too. You're only human, so don't beat yourself up too bad, when these things happen. Now all that being said, if you and your husband are committed to keeping his mom in your home, then perhaps it's time to be talking about hiring some outside help in to assist you during the day. That way you can get out and about for a few hours to do the things you enjoy, and that will certainly help your stress level as well. That is the most important thing to do, is take care of yourself first, or you cannot take care of anyone else properly. Sadly that is the biggest mistake caregivers make, not taking care of themselves. Most of us have learned that the hard way, but thankfully we eventually did learn it. So be kind to yourself, and know you're doing the best you can. If over time it just gets to be too much(as she will only continue to get worse), then it perhaps will be time to be looking for the appropriate facility for her to go to. Wishing you the best.

It’s wrong of your husband to expect this of you, it’s his mother not yours, and it certainly sounds like she needs more care than one person can provide. Besides, with all the tension in the house, it’s not a good atmosphere for anyone involved. Time for an honest talk with your husband, the living arrangements aren’t working well and a new plan is needed. Can more help be brought in? Would her needs be better served elsewhere?