I have to preface this by saying that I'm a DIL who doesn't get along with my MIL. So I am more able to see this from a DIL perspective. My goal is not-so-much to 'take up' for the DIL, but more to give you a DIL perspective. Cool?
I think you should talk to your DS and DIL and ask them how to help THEM. Because if you "do things wrong" then you're not actually helping, you're often making MORE work for them. (For example: if you don't load the dishwasher 'correctly' and some of the dishes don't get clean, and need to be re-done. Theoretically, it's helpful to load the dishwasher for them, but in reality, it's making more work.)
So talk to THEM and find out what THEY want from you. Then figure out what you're willing to give and do it.
I have to say that I was troubled by your statement of being a "full time Grandma". I think you'd be better off having your own complete life, and then negotiating the time with DS and DIL. Do you know what a Venne Diagram is? Their life is one circle, your life is another, you have to negotiate the overlapped areas between the two - your circle can't be completely INSIDE their circle, it just won't work.
Now, all that being said, going from 1 to 2 is HARD, and 3 months is still early days in figuring all that out. Please give her more time to work it out. The more understanding you are right now, the better your chances of a continued and good relationship with your DIL, your DS and your DGK's.