Can my mother in law claim her mother in law suite as hers?

Assuming your mother in law isn't on the title to the property, she owns nothing. She might have a claim for unjust enrichment if your give her the boot and if she could prove you promised to let her live there for a certain period of time. Any agreement that she can prove can be enforced but owning the property gives you the upper hand.   Family fights are pretty ugly in Court and can damage relations for a long time so it's a situation you want to work out privately if at all possible.