It's all just family dynamics - I've seen the same with people I know well in Germany, the states, in Turkey and Portugal. Some families are incredibly tight knit and meddle endlessly, they mean well, they care, but they do not know what boundaries are, much less respect them.
I've seen it cause hurt and tears and all sorts of untold trouble on both sides. The best advice I can give you is to be kind and find a way to out- maneuver the grandparents interference. Don't shut them out, but do let them know if they overstepped - which they will continue to do for a few years until one day you have come to an understanding.
It is a process and this is just the beginning.
Seeing some of the damage, interfering and shutting out can do was a strong motivation for me to consider how to deal with my own DIL. Believe me I gritted my teeth a time or two, but there were two things in the back of my mind that kept me from overstepping. I want to have access to my son and his family and of course my grandchildren - I've seen DILs who use their children as a weapon - withhold son and grandkid.
It is hard enough as a mother to let go of your kid, but you don't want to become estranged, because you can't stay out of their business. It is a new experience for the parents too to become grandparents, it is a joy. There is an adjustment period - you'll sort it out.
The second reason not to interfere is how it will effect your children/grandchildren in the years to come. Family dynamics change all the time, don't ever let things escalate beyond repair - it can.
Consider this - one day you will be the grandparent and your son or daughter will let you into their new family - or not. How hurt would you be?
Both my Mom and my MIL were two to five thousand miles away when I had my son and in my case they were both capable women and I would have loved some "interference" from them. Instead I was totally alone with a newborn for six weeks while my husband was on military maneuvers. Perspective baby - perspective:)
Count your blessings - make it work and yes, they all love you, they all have their own plans and expectations for you:) - but it is OK to remind them that your life and your decisions are your own. Don't lose your cool or your perspective and yes, it is smart to supervise a mom who is known to leave on the gas - good luck!:)
PS - I like the 'call once a day' idea - but will add that my own family is considered cold by many and calling more than once every four weeks would prompt my mother to say, "What's wrong, why do you keep calling me?"
Family - go figure:)