YOU SAID:
my mum's mum is a mum for my mum
INTO JAPANESE
私のお母さんのお母さんは私のお母さんのお母さんです
BACK INTO ENGLISH
My mom's mom is my mom's mom
INTO JAPANESE
私のお母さんのお母さんは私のお母さんのお母さんです
BACK INTO ENGLISH
My mom's mom is my mom's mom
That didn't even make that much sense in English.