We know Kelly is telling the truth because he obviously watched the show at some point during those 20 years. We saw what Kelly was talking about rather just listen to him tell a story and taking his word for it.
I think it's a safe bet that the airstream belonged to Nick. His legacy was passed on to Diana and Kelly. Whether it belongs to him currently or not isn't an issue because the legacy is what matters. Diana and Kelly having ownership of it doesn't change it.
I understand your curiosity but I wouldn't be confident that Kelly wrote about how his mom and dad got together. Grimms really didn't write about their origin stories. There was a lineage book but there was nothing telling the audience that past Grimms wrote about how their parents hooked up. I don't get the impression that family trees detail how everyone's ancestors met and how their relationship developed.
I think it's a safe bet that the airstream belonged to Nick. His legacy was passed on to Diana and Kelly. Whether it belongs to him currently or not isn't an issue because the legacy is what matters. Diana and Kelly having ownership of it doesn't change it.
I understand your curiosity but I wouldn't be confident that Kelly wrote about how his mom and dad got together. Grimms really didn't write about their origin stories. There was a lineage book but there was nothing telling the audience that past Grimms wrote about how their parents hooked up. I don't get the impression that family trees detail how everyone's ancestors met and how their relationship developed.