K., one thing to remember is that the Mother and Father may chose to do things differently than you did them thus the great saying "Do what is best for YOU and YOUR family"
I say this as I have been a mom for almost 20 yrs... my first MIL catered to her son, I could do nothing right. I got blessed to be married to a wonderful man and this MIL is a blessing. I will share that I know she bites her tongue and I hope I can be as good as she is when my son marries but I have a DD with my DH and I don't do things like SIL or others, I do what I need to do for MY family. For example, I nursed till my DD was 2, coslept till she was 3, and I now HS and work very PT on the weekends.... Something she didn't do as she was an RN and SIL is in corporate America... I value different things, money is important and we live comfortably maybe I don't have that Coach handbag or go on a big vacation every year... I myself like the simpler things in life, funny though as my DH is on the same page as I am.
MIL probably isn't too happy with some of our decisions BUT WE do what is BEST for OUR family.
If you are the grandparent and you can respect that, then you will be fine, off to watch the children, if the parents need to go out, some women are much more maternal than others, some can't wait to get away from their children (sounds harsh but true) and some don't want them out of their sight.
I will also share that MIL took 2 wks off when I had DD to be there but I suppose when I think in retrospect, I nursed and what not so there wasn't a lot I needed done.. I regret that now almost 6 yrs later, I really wish I would have invited her over more and just let her hold DD... I suppose, I just waited a long 14 yrs to get our DD and didn't want to leave her when she was a baby.
There are a ton of grandparenting books available you may want to check them out. Things have changed and I say that honestly as I have a soon to be 20 yr old and a 5 yr old...
Make sure you are up to date on all of the new safety regulations and check with mom on just about everything, she needs to be confident and encouraged if this is her first child... but of course with any suggestions also add that she needs to make the best decision for her family.
This way YOU being the grandparent can suggest something that might be helpful but she needs to make the decision if it works best for her and her family, and don't get upset or feel rejected if she doesn't do it your way or what you suggested.
Remember too K., that you can buy things if you want, you can keep them at your house too... this encourages them to bring the baby over more for a visit and they will feel more secure that your house is baby proof... and child ready. :)
Congrats!