Is it cool or acceptable to invite the groom's mother to the wedding through verbal invitation only?

I'm hoping she's just so distracted and flustered with wedding preparations that she's not thinking clearly. I would talk to your son, not your future daughter-in-law (that seems to make things go more smoothly). Explain that you were hurt not to receive an invitation, and that you would like one as a keepsake. It's not at all an unreasonable request.