I lost my dad a few years back and received a substantial, life changing inheritance. I also am left with feelings of regret, sorrow and frustration because my father was a very flawed person and we had a very complicated relationship, but I loved him very much. He was a full-blown "as seen on TV" hoarder, had grown up extremely poor (which I think had a hand in him turning into a hoarder - he obsessed over food and clothing), and also had some undiagnosed mental issues (OCD? OCPD?) that made it hard to even try to talk to him about certain things.
That being said, I basically did nothing for about a year after inheriting. I'd advise you to do the same. The money isn't going to be hurt sitting around for a while on auto-pilot while you grieve and come to terms with your loss. But I think that your idea of setting up a scholarship fund or donating to a charity (or even creating a charitable trust) in your mother's memory would be a wonderful idea if you don't need the money and your children are well set in life.
And I wouldn't worry about what your friends or other family members would do if it was them or their advice on the matter. You do what you feel you need to do - and what you think will make you happy. That is all that matters.
I have no kids, so I decided that the funds would be used for supporting myself and my husband for our lifetimes, after our death, the money is going half to to charity, and the other half will be to create a scholarship in my father's name at the college he received his degree, to benefit children from underprivileged families. There may be more details to work out (need to contact the college and do some more research), but that's what sounds good to me and I love the idea that my dad's name will be around forever because of a scholarship.
I am so very sorry for your loss. Be gentle with yourself and your family about all of this. Please don't feel like you have to satisfy any other person's ideas of what your grief process should look like, or how you need to be using the inheritance she left you. Please be assured that most people really think what you're planning is a beautiful, amazing thing - and no one in their right mind is going to judge you as doing the wrong thing if you go forward with your plans, and if they do, they are 100% in the wrong and you shouldn't worry a second about even keeping that type of person in your life anyway. ;)