I don't think so. This classmate knew your mother's brother... he's free to share his memories with whomever he wants. You're free to ask. I wouldn't pester the classmate if he doesn't want to talk, but there's not anything wrong with asking him to see if he can share. I would think most people would be sympathetic to what you're asking, as long as they're in a place where they feel ok to talk. If I were the classmate, I wouldn't feel bothered by the request... If I were your mother, well, as Nightside of Eden said.. if she finds out and is upset, that's her issue, not yours.

That said... personally, I wouldn't use any info from the classmate to try to spark conversations with your mom, for the reasons already discussed... it would be painful to her.

I hope your able to get more information from the classmate, or your extended family... good luck.