My 51-year-old daughter is an MSA patient in the 3rd year. Would she be better off in a facility?

Yes.

Are you able to safely care for her without caregivers?
Can the number of caregiver hours be increased to make it easier for you to do what you need to on your own?
It sounds like she needs more care than you can provide yourself.
The options are limited I would think.
Assisted Living but her care needs might be more than they can manage in AL.
Group Home. That might be an option but again her care maybe more than they can manage.
A Small home like facility might be the best option if there are any in your area.
Skilled Nursing facility would be the last option. Search "Sheltered Care Home"

If she has a case worker find out if the caregiver hours can be increased. You can also discuss the facility options that are available in your area.
This is also a discussion to have with her. If her care is getting to be more than you can manage she needs to know that.

If she needs more care than can reasonably be provided in a home setting and she needs a team of caregivers then she needs nursing home level care. During my mom’s nursing home years there were quite a few younger residents, all making the best of harsh medical conditions. I’m sorry you and your daughter are facing this and wish you both peace

This is a hard decision. Do you care for her? Sounds to me she needs 24/7 care and she won't get that in an Assisted Living residence. It would mean LTC. I would say your at least in your 70s. I am 76 and if it was me, I would place her if no one is there to care for her. You will not be here forever.