What happens if I am the main caregiver and my brother or sister move my mother into a nursing home too far away for me to visit?

Do you think your brother or sister are likely to suggest moving your mother so far away from you? Have you discussed what sort of placement would be best for your mother with them?

In any case, I second CW's point. Sharing and consultation are great, but in the end it's impractical to split guardianship effectively three ways - it just makes the whole job pointlessly complicated.

Would your brother and sister have a problem if you were your mother's guardian?

Also, where are you? Different countries have different rules for guardianship.

Even though sharing is portrayed to be the best way to do things real life isn't always suited to democracy, it would be better that one person is in charge (you) and the others named as secondaries.