Understanding my son's girlfriend

It is you who is putting up the barrier Frannyannie by insisting on taking your dog. She is quite right to state her own house rules. If you want to see your GC then you must play by her house rules. Are you really prepared to let a dog come between you and time with your GC? If you feel "left out" then it is your choice and your doing.

You are going to have to choose what is most important to you: dog or GC.

This is a non-problem - you are creating a problem where none needs to be.

I say no to anyone who wants to visit here with a dog. Our house, our rules.

DD and SILs best friends have two little dogs, nice enough but not used to children.
When DGS visits them the dogs go to visit friends Mother and they do not bring them to visit here, or take them with them when they take DGS out.
The safety and welfare of the child comes first.
Even the most placid dog can become nervous around a crawling or toddling child.

Sorry if this sounds harsh but her house/child her rules, surely seeing your grandchild takes priority over the dog . Find a way to go and see them lots of suggestions above.

Why can't you leave the dog in the car for a while when you visit and take it in turns to walk him? There are some diseases children can catch from dogs which might be what is worrying her. I think one causes blindness.

It is normal for a young mum to be over protective and she might well feel you are putting your dog before her child.

Has she been diagnosed with OCD or is it just that you think she is? If she has then she needs help and support.

imo you could be more understanding.

Tricky one, do you not have a friend who would have the dog for a few hours. 40miles is doable in a day. Or maybe a neighbour could pop in a couple of times to see to your dog.
Failing that, the only solution I can think of is if you both drive is for you and DH to take turns visiting DS family. Not ideal I know, and it's a shame you can't all be together. Would they not visit you ? Her house her rules I'm afraid.