Well, you should introduce her as she is, your girlfriend. You shouldn't care what other people think. Unless, she doesn't want you to. Then, there's something going on. Whether she's just nervous or something else.
Married or not your son's and his girlfriend's son is still your biological grandson so introduce your son's son as your grandson. These days there are more younger people living together and it is not that much of a stigmatism any longer. Be proud of your grandson!
Biologists must be careful not to accidentally introduce new species into an ecosystem. You should always introduce yourself when meeting new people.
going out and meeting people
Convention
Convention
Convention or venue will work.
because they wanted to
Market
The noun 'meeting' is a word for:a public gathering of people for a specific purpose;two or more people coming together for a specific purpose;an encounter.
Usually the people meeting convene together physically within a designated area
If you're referring to a group of people meeting to discuss solemn matters, I'd say "convocation" or "council" even. If you're referring to two people meeting and feeling solemn together in meeting I'd refer to it as a confrontation. And then there is also "funeral" which is a pretty solemn meeting, I'd say.
It means that you and him will be going together and both of you will not be seeing other people.