Does anyone know if there is a word, in English or any other language, to express the relationship between mothers-in-law other than saying, "she is my daughter's mother-in-law"? Seems like a simpler word or phrase would have been invented by now. Same for fathers-in-law.

Not in English, but in Yiddish there is. It's machitunim, or a similar transliteration. The -ch- is pronounced as in Johann Sebastian Bach; the accent is on -TUN-, and the -im denotes plural (the relationship is commutative).

Here's one expanded reference.

WELCOME raynbeaugirl.

WAY TO GO, DOC: very impressive

Thanks so much. I just knew there had to be a term out there. Happy Day! Linda