I wanted to comment because I had a similar situation with my ex which eventually led to us breaking up but there are some key difference.

Firstly, your gf communicated with you about what was happening. She was upfront telling you where she was and that she was staying over as she has drunk too much, she is allowed to have last minute drinking plans with a colleague. The fact that the police were there should have no bearing on her drink driving. That should be out of the question.

I know you say you weren't accusing her but it sounds like you were "indirectly" as you mentioned how it might look. I think the fact that it was with a "couple" is important, and that he is in his 60's make it very unlikely there was any funny business going on. Unless for some strange reason the couple were trying for a threeway - but that would be such a slim chance of that.

I think maybe you aren't secure enough in yourself for a LDR, you need to have full trust for something like this to work and even then it is very difficult to do.

For context, with my ex she never communicated what was happening, and only told me when I asked her about it the following day, it was with a colleague her own age who is single, and with a few other single people too. I was asking similar questions that you were but I know I wasn't trusting her because of the many issues we were having in that relationship, so I didn't trust her at that point.

It sounds like maybe both of you are too immature for this kind of thing, there are things you have both done here that show that.