At last! I've found the word. My son got married, I am a mother-in-law. I have a wonderful daughter-in-law and she in turn has a mother who I dearly love. What is the name for our relationship? Co-MILs? icky; my son's MIL? that's his relationship, not mine; my DIL's mother? again her relationship, not mine.
I have asked many people and finally found an answer from a friend then confirmed it with an internet search. In Yiddish she is my makheteynesta.
Along with the joy of knowing the word is the knowledge that it is not negative in any way. In my non Jewish culture MIL and DIL are often words that come pre-loaded with negative connotations. The word "makheteynesta" carries no such burden.
The relationship I have with my Makheteynesta Donna, is our relationship, not my son's nor her daughter's.
"A similar male in-law relationship is called makhuten. Otherwise, in English, the same problems exist for both sexes; men experience an analogous lack of appropriate verbal identifiers."1
The "plural covering both sexes"1 or as one source said, "the entire extended family" 2 is makhetunim.
In Conclusion:
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"makheteneste your daughter or son's mother-in-law" 2
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"machuten (mekhutn) your daughter or son's father-in-law" 2
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"makhetunim your spouse's extended family" 2or your daughter or son's in-laws 1
SOURCES online:
1 http://www.drexel.edu/doj/archives/2002/essay/kotzin_callherrose.asp
2 http://www.asinine.com/essays/yiddish.html
The spelling variations are as appeared in the original sources.
DejaMorgana has a wonderful alternative
affine which is a bit easier to pronounce although still, it is Latin! I think the best may be "Law-Kin" which I just found in a book written in the 60s by a lady from the US south but about gardening in Vermont. I'm not sure of the origin, southern or New England but I LIKE that word! She defines it as one's childrens' inlaws.