That's probably a bug, you should only be blocked from removing a connections if it would spit the tree.
Anyway here's a work around.
On the cousin select More actions... then Set parents. Select a person that's already on the tree as a second or third parent (preferable someone with out any partners so the other slot doesn't get auto filled) confirm your choice with Ok. Then Select More actions... again, but this time select Change partners/friends, the option to remove the friendship to the mother should be available.
After you remove the friendship you can remove the person you set as a parent from the parent list.