It's good to see from your posts PurpleSneakers that although you're finding your m.i.l.'s desire to see and help care for her GC over bearing, you also want to handle the situation with compassion and understanding.
You said in an earlier post that her tendency to be over bearing is noted by her other AC and they're relieved that it's you whose had the first GC. I wonder then if her approach has taken you and your DH completely by surprise or if to some extent you hadn't seen this coming. I also wonder if the intensity of her questioning has always been a factor but with your hands full with your first child, you are more aware of it than you were in the past.
I remember before our first GC was born, my friends telling me I'd probably be taken aback by the overwhelming love I'd feel the first time I ever saw him. They were right, even though they'd told me, it still took me by complete surprise; it will have been the same for your m.i.l. too.
Although not wanted at the moment, there may come a time when you will be grateful of her offer to do overnight baby sitting, giving you and your DH a well deserved rest, possibly giving you the chance to have a night away. There is a degree of geographical distance so that prevents her from popping in unannounced and/or uninvited so it's not as if you have no way of tempering her enthusiasm. I appreciate that long 'phone calls can be as infuriating as unexpected visitors, but at least when on the 'phone you can easily bring the conversation to an end by saying 'I've got to go, there's someone at the door; I was just on my way out; the baby's crying'.
I was upset to read that your DH has "reduced contact". Does her over enthusiasm and her inability to recognise this in herself, as annoying as it must be, really necessitate her having reduced contact with her son? Wont this make the matter worse, fueling insecurities and intensifying her need for contact?
I'm sticking my head above the parapet and joining you NannandGrampy regarding Lillie's post. GC aren't treats to be dolled out as a reward for what their parents perceive to be 'good behaviour' on the part of the GP's. Perhaps if that's how they're sometimes viewed, that's why some are taken away from their GP's as a punishment for what parents regard as 'bad behaviour'.
Please be careful. Almost 5 years ago our ES told us he needed 'some space', we gave it. Seven months later we were cut out of his and our only GC's lives; that was 4.5 years ago. Rather than reducing contact, keep the lines of communication open, no matter how frustrating that may be.
I hope you'll be able to find a way of working through your difficulties that enables all of you to enjoy this relatively new addition to your family. I hope too, that if she isn't already aware of her d.i.l.'s kindness and her willingness to find the best possible outcome, one day she'll know how fortunate she is that you are that d.i.l.