I am a live-in aide for my grandmother. Is there any way that her children could take her away and put her in a nursing home?

The person who has Medical POA (not financial/legal POA) can place grandma in a care center if he/she deems it in her best interest medically.

I take it that you think GM can remain at home, and the generation above you does not. Is that it? Can you tell us the reasoning on both sides?

Who is POA? - that is the person otherwise they need to go to authorities to get guardianship - maybe do this first -

Are you salaried? - make sure you pay whatever taxes you need to do in your country to start getting your own retirement in line as it is never to early to start! - Grannie has lived long & 1/4 of your genes come from her so chances are you will too

As long as you are able to keep up the pace of caring for your Grandmother, there would be no need for anyone to place her in a nursing home. But we need to view reality.... Grandmother will start developing other issues beside not being mobile [as per your profile].

Then it would be difficult for you to do all the work that 3 full-time caregivers do in one day, each working an 8 hour shift.

One question, how are you funding your own retirement? Is Grandmother paying you so that you have some income coming in?