J.H.
I suggest offering specific ideas to your friend on how you'd like to help. Perhaps bring over a nice cooked meal (a casserole or something) so that her family can eat without her having to worry about cooking - I have a great recipe for a 5 cheese pasta that can be heated and re-heated for leftovers - I've brought it to friends after they have babies and they love it (both adults and young kids like it so that's helpful too). I usually pair it with a basket that contains a salad and bread for sides and maybe some brownies for dessert.
Or maybe you can offer to watch her kids if she needs to get out and just have a "me" day (maybe she can visit her mom's gravesite to spend some time grieving or just get out and walk around the mall to clear her head). I have a very close friend who lost her 4 year old nephew last year and it was incredibly hard on her family. At the time, I made specific offers to take care of my friend's daughter while she helped her family through different things and she was incredibly appreciative. When I originally just told her, "let me know what I can do", she said thank you but she didn't really respond. But when I said "Can I watch your daughter this afternoon for you while you do X, Y, and Z", she took me up on the offer. The way I included my own daughter so that she didn't feel left out is that I brought my daughter with me to play with her daughter while I was babysitting. This is a good way to show your support, especially when you don't really know what your friend is going through (since you haven't experienced it yourself).