Thank you all so very much for your helpful comments.
I have got an animal and that is one of the 'problems'. I got a labrador pup when I retired and my DIL does not like dog hair. After nearly three years my son started bringing my grandson at the weekends when he can but he works during the week so has other things to do at the weekend. Unfortunately my DIL has many anxieties/phobias and won't leave my grandchild anywhere. She works at home a few hours a week as a telephonist - sort of call centre work. Weather permitting I can take my grandchild to the swings and for a walk around the area. However, I would love to take him swimming. My DIL has a fear of water and that is something I could do. I'd like to take him to the library, soft play, parks but apart from his parents, no body ever has. I can't have him in my car so I am not able to pick him up or take him to play school where he's been going since he was two years old. I can't take him on the bus. I've been going round regularly since he was born in 2014 but only once a week.
On two occasions I've been with my DIL and grandson to soft play and once to the park. That's in three years. I've suggested other places but nothing has ever happened.
It's not just a wish to have him in my house, it's the longing, I suppose, to have him in my life - just occasionally and that would include my house.
They live about two miles away so it's not difficult for me to get there.
I have got two four foot dog/child gates that I had installed before he was born and apart from having locks on certain cupboard doors and the covers for sockets, I haven't done anything to childproof the house as he doesn't come.
I have explained how I feel and I know my DIL's anxieties and there we are.
Actually, I have never been asked to look after my grand son. I started off by turning up when he was a baby and keeping an eye on him while his mum could get on with what she needed to do. Then, after 9 months and chose not to return to work, I continued going round to look after my gs (not sure of abbreviations yet) to coincide with her shifts - a couple of times a week.
Again, thanks for your comments which I'll read again as I know I've not mentioned many points.