I totally agree with you, though Narmada was not correct today but whatever happen was her reaction that came out bcoz of the fear of loosing her child...
1. Narmada respects her Jijji a lot but still she has been supporting Imlie right from the day she entered the story, so today when she actually sensed BMs word making some sense..she couldn't control..and I believe she would have done the same with Aru if Imlies life was in danger...Afterall she tried to stop them from going...
2. Arpita and Aryan never lied to her so she couldn't think that Imlie will lie to her for what so ever reason and believed he words...Although I think Imlie should have been honest to her at that point bcoz this would have been pacifying to the family in such a situation...
3. Narmada has been in a similar situation in the past; and as we have seen how she considers both her kids and their partners as her own children (Mere Bacche)...We can imagine how she must have felt as a mother when Arvind when went for work and never returned...And what happens after that we all know...the whole family was traumatized for years!!
So naturally Aru's fatal conditioned triggered her worst memories...
Although her slap cannot be justified but I think Narmada's and Imlie's relationship is not just a normal DIL-MIL relationship, Imlie has always considered her Kaki Maa as a motherly figure.... She stood for Imlie, she would send tiffin for Imlie just like she did for her son Aryan!! We have seen her worried for Imlie's life and realtionship with Aditya just like a mother. So today if she slapped her for being careless with herself and Aru's life, I can understand her emotions.....
Yes it is domestic violence lawfully which is not supportable at all, but I think their relationship is no less than a mother-daughter.....When it comes to mother in law, we mostly take it in a bad way....But we should not forget the relationship Imlie and Narmada shares...So yeah she can be a bit strict to 'Her Imlie' as a mom...