Yes, I would allow a train on the slide. Whether or not I stopped my child from doing it when one parent didn't want the kids to do it would depend on the number of children involved. For example in this situation if there were 6 kids doing it and the grandparents wanted their 2 to stop I'd probably allow the train to continue, monitoring so that the two singles could also slide alone.
I think you did the right things. I'm especially impressed at how you made going home about not following your instructions.
A couple of times I've had a parent tell M. to stop my daughter from climbing up the outside of a covered slide. The cover has projections so that it's easy to climb. I told them that she was OK. I wondered if I should've stopped her because other kids might want to climb when their parents didn't want them to. In the end I decided I was glad that I let her climb. The parent who didn't want his kid to climb told him no and he didn't climb. A couple more kids also climbed. This is one of those lessons in life. ie. parents get to decide and all your life there will be something that some people can do and others can't
I was a bit surprised when a couple of parents told M. climbing wasn't safe. It seems that kids are not allowed to do so many adventurous things that have been done for years because every once in awhile a kid does get hurt. No tree climbing. No monkey bars. no teeter totters. Now in our city parks, no slide, no merry go round. The park closest to us only has swings. The school playground doesn't have swings but does have monkey bars. I wish that the equipment was there to let the parent decide. I am aware that it's most likely this way because of law suits.