You've gotten some great advice already. I think you'll just have to be patient with the mom and understand that she's under stress, she's got 2 babies, is just a kid herself, is tired, and has hormones going crazy. Plus, it is Winter, and the babies were probably early. The doctor probably recommended that they don't go anywhere for at least 8 weeks.
At least they have given you a timeframe, and you're only 5 weeks away now. I know it is hard when you've planned a nursery and want to spend time with your grandkids, but it will come. This is going to be a lifelong relationship with that mother, so you really need to try your best to be understanding and give her extra slack right now. The good thing is that she is trying to do what is in the best interest of the babies, so that's a really good thing.
As long as she isn't dragging them all over the place unnecessarily, I think you should be patient and just go over to see them and help out. It will take her some time to know that you are able to care for them and know their routines, etc. I'm sure as they get older you'll see them more and more. I'm glad they are letting your son over to see the babies- that says a lot. Hopefully when they are several months old they will start letting you take them. I would start off with taking them a few hours during the day, and work your way up to taking them overnight. That will be less traumatic on the mom. There is something weird about your baby not being with you, even if you know they are being taken care of.
My parents went through the same thing with my brother's child. At first they weren't allowed to have my nephew over at all, then rarely, then more often and sometime after he turned 1, the mom relaxed and they got to see him all the time, even for a whole weekend.
I hope this helps and gives you hope that things will work out just fine...even if it wasn't what you had planned.