I lost my father when I was 7. My brother was 11 and my sister was 15. It was tough (like that's a surprise). I remember people trying so hard to distract me. Taking me to movies. My grandmother who was very traditional (and this was in 1972 so a long time ago in different times) bought me a bikini! Which was about as much unlike her as anything and I remember thinking "wow, people will do about anything to make me happy". But what I really wanted and needed was someone to talk frank with me about my loss. A kid, even a young kid can only be distracted for so long. All the movies, ice cream, trips to Six Flags and the pool, couldn't really heal me. But in those days counseling was very unusual. We didn't ever get any, didn't go to grief support and after a coupe of months, it was rare for anyone outside family to mention or acknowledge what he had been through. Years later I came to realize that many of the choices I made from the minute my dad died reflected what I had been through and what I hadn't (namely counseling).
This book really helped me and my brother:
http://www.amazon.com/Loss-That-For...=sr_1_1?ie=UTF8&s=books&qid=1266431094&sr=1-1
Its called the Loss That Lasts Forever. It helped me and its been awhile so I can't comment on if this book would help a child of 10. But maybe mom can read it? Or you can to understand and help this little girl. If you check out that link, there are other books about losing a dad.
Also, most hospices have grief support for kids and while its the mom's call, I hope she'll consider it. Really and truly, even if a kid appears fine after this type of loss, its so life changing and so heart breaking, it can have affects for years if not handled right in the first months and years.
My best advice is to surround this little girl with love. Support her and tell her how sorry you are. Don't avoid talking about what she is going through altogether. If she says at some point she doesn't want to talk about it, abide by that but leave the door open.
And she will laugh. Kids are very resiliant. But she'll have bad days too. And thats when if she knows she can come to you and talk about dad, it will be priceless for her. I think its great if she can come over and be with a family (yours) where she can be herself. If she wants to talk, let her and listen. I so remember once trying to talk about my dad and my friend's mom saying something to the affect of "oh you just need to be strong and move on". Again, this was a long time ago. Just follow her lead. If she wants to laugh and not talk, that's okay, if she needs to, listen and let her know you are there for her.
Not sure any of that helps but just thought I'd share! I'll say a prayer for this little girl and for you, its tough to support a child through this. I've done that too and its just so sad to see it happening but also God puts people in the place they need to be and I think this little girl is lucky to have someone who clearly is thinking and caring ahead!
