I can't remember the episodes that well but didn't Mindy meet Monica in the build up to getting Rachel to be a bridesmaid? Couldn't she just have invited her (to help seal the deal with Rachel).

I would say it's plausible.

Consider the daffodil. And while you're doing that I'll be over here looking through your stuff.

I still believe it to be plausible. We can actually just agree to disagree on this

That's fine if that's the explanation you come up with, but it's not really plausible. It's really reaching.

Thank you. I know there is nothing directly said about it, but it's the only explanation that makes sense to me from the information we have. It's not like the theory changes a character, or shows someone in a negative light. As viewers, sometimes we're left to fill in the blanks. It's not anything all that important, but I prefer to think of an explanation and just enjoy the show.

There's nothing in the show to support it, but it isn't hard to believe that's the reason. I do agree the writers didn't plan out a reason, but since you could explain it with possibilities, it doesn't bother me as something impossible.

Consider the daffodil. And while you're doing that I'll be over here looking through your stuff.

There's nothing to support that. Richard is friends with Monica's parents. How does that have anything to do with Barry or Mindy? Just because he's friends with Monica's parents he automatically knows other parents too? Monica didn't know or live near Barry or Mindy.

I thought it was quite plausible that they were there. Richard is friends with the other parents in the area, and was probably invited for that reason. And Monica was his date.
I had friends of my in laws at my wedding, who I met for the first time at my wedding. As Rachel, Monica and Ross had mentioned, Richard was around during their childhood.

This comes up a lot.
As stated, no clear reason is given. It is obviously shoehorned in for the sake of the story and flow of the episode.
One popular theory seems to be that as Richard was an eye doctor and Barry was an orthodontist, both from vaguely the same area, that they (and their families) may have known each other and Monica was simply Richard's plus one.

There is no plausible in show explanation. It was just more continent writing.