When I decided on NC with my mother, my DH and I discussed it and allowed my parents contact with my DC very sparingly. She still started in on them with her abuse, just as she had done with myself and my brother including a pretty serious safety incident on their part involving my DC (because my parents, especially my mother, do not actually care one single jot about them and only saw them as a means to get at me) when DH spoke to them about it my parents spat their dummy out and decided to have no contact with my DC.
They did try and resume contact a few times after that when they thought things had calmed down enough but they were fully and completely ignored via every single means of contact including the flying monkeys of which there were many.
My youngest was 5 and my eldest was 7 and we explained to them in an age appropriate way that my mother was not a kind woman to me and as she and my father had put them in danger (both mentally and physically) we have decided that it is not safe for you to be around them any more.
As my DC got older and asked about my parents, we explained again and went into more detail about the situation. All done with their ages in mind and yes they still ask about my parents (DC are now 10 and 12) but again DH and I just explain what we have already said and invited our DC to talk to us about how they feel about it and ask any questions when they feel the need.
I and DH like you thought we were doing the best thing for all concerned by still allowing contact, although sparingly, and we can both see now that it was absolutely the wrong decision.
You are at the beginning of the NC journey, there will be ups and downs, mistakes will be made but it is completely normal. If my experience is anything to go by you may go through the stages of grief while you mourn the mother you never had. It is not easy, almost 6 years on for me and I still have difficult days. Mothers day is a big one for me, I get to mourn the mother I never had and get to enjoy the relationship with my girls it's a double edged sword.
Another piece of advice I can give is to not care, I know it is fucking hard, but you have to learn not to care what others (your mothers family and friends) think. It took me a couple of years of being embarrassed about being NC (when I saw my mothers friends out and about) but now I don't give a flying crap and it is soooooo much easier.
Full NC have brought a calm rationality to my life and I have gone onwards and upwards once I was able to get her out of my life and head. My self esteem is no longer rock bottom, my self hatred has gone, my self doubt is much less and my mental health is the best it has ever been. Full NC being no contact at all, not even in response to her or her flying monkeys, not opening letters (I kept mine incase I needed to speak to police re harassment, luckily I've had no contact from her in over 2 years now).
If there are any questions I can answer for you please let me know.