Yup, he is definitely coping a feel, but she doesn't seem to care or get angry about it. 
You know, I've been looking at pictures of her husband, the few that I can find, and I think that might be him, Carl Dean. If so, that'll be the first time I've ever seen him in a public appearance with Dolly.
Yeah, I was looking at some photos and young Carl Dean and old Carl Dean share much the same facial features. Yup, he has a big gut now compared to his youth, but that is not unusual. 
The original video being from the 2019 London 9 to 5: The Musical gala, I was going to make a joke how the man, taking liberties he does not have, is soon going to find himself tied up in an empty warehouse.
The man is not identified in the video or on the page where it appears, and he does arrive with another woman I cropped out from the gif. However if he is the husband, it is funny in another way - even if inappropriate in public, he just holds Dolly like he always does. Life can be good...