Congratulations Imperfect! What a wonderful time in your life! Enjoy!
I'm not sure if you're "learning that a new set of boundaries is in place" cuz of reactions from DD and SIL or cuz of ideas you've heard/read. But either way, I'm going to chime in with others to say that just the fact that you've come here to ask these questions shows you're on the right track!
And yes, you are quite right - IME, new parents want to figure things out for themselves without unsolicited advice (especially perhaps from their parents/PILs - sigh -). Often, in fact, they turn to friends, professionals or the Internet for any advice, if they want it, rather than their own parents/PILs. That's partly cuz a lot has changed since our day, as you may or may not know - newborns put to sleep on their backs or sides, instead of tummies, no heavy blankets used till after about a year and so forth. As experienced as we are, there are some new and crucial things we just don't know.
I'm glad you bit your tongue rather than suggesting that DD turn her phone off. And I agree with the idea that you should continue to keep any advice to yourself, unless asked for it (except perhaps, in the case of a true emergency). If you really feel you need to say something, I also agree that doing so in the form of a question ("Have you thought about...?") is better than saying "You should/shouldn't..." and so forth. But, mostly, especially in these early days, I think it's better to wait and see if they ask you. Want to add, too, as the mother of two DDs, that no, they are not always more open to advice from us than DILs would be - some are but others are not. So you are wise to tread carefully, IMO, and take your cues from your own DD.
Also, since guys, nowadays, are often more involved in childcare, many new parents, I find, want to keep those early days to themselves to work out their routines and bond as a family unit. So yes, please do continue to wait till invited to see baby, whether at the hospital or their home. And yes, I agree with the idea of asking if you can help in any way (if you are truly up for that), but also with accepting it graciously if they decline.
Please remember, too, that they may wish you to help with household chores more than with baby. If you're not up for that - or not up for helping, period - please keep any visits brief and just enjoy whatever time you get with them and that new baby.
It may take some time for you to get used to your new role - it did for me and many other GPs I know. But please remember, the new parents are feeling their way, too. Please give them however much space they seem to need and realize they may change a bit, as time goes on.
Sorry this is getting long. But just want to add I think you're going to be a wonderful GM and continue to have great relations with DD and SIL! Best wishes to all!