How do I know when to put my mother in memory care?

When you have to ask the question, that's when you know it's time or more than likely past time.

You say in your profile that mom had Alzheimer's / dementia.
Has she actually been diagnosed? Because further in your profile you say you are wondering if you should have her tested before placing her in Memory Care.
Are you POA for health and or finances? Do you have the legal authority to place her in Memory Care?
When to place her is or can be a complicated answer. The easiest answer is when it is no longer safe for her to remain at home.
If she can "escape"
If she turns off things that should be left on (refrigerator, furnace for example)
If she leaves things on that should be off (stove, water for example)
If it is no longer safe for you to care for her. If you get hurt caring for her who cares for you.
If there is a possibility that you could hurt her.
If she is a fall risk
If she can get violent.
Just to list a few.
But before anything you need to be sure you have the authority to place her.

If you ask Google that question you'll find a lot of advice, including this AgingCare article

https://www.agingcare.com/articles/when-is-it-time-to-place-a-loved-one-with-dementia-188309.htm