Take them all to the pool or beach. The kid with the broken finger will get plenty of attention at the pool or beach. All the other kids will envy the bandage or cast and wish they had something broken! I always wished I had a broken something when I was kid, and stared jealously at any kids with bandages or casts or crutches.
Sick kids should be resting and convalescing, not participating in family activities. It's tough, but it's real life. Several years ago, I caught the flu--the real influenza, the stuff we get shots to protect ourselves from (except I didn't get a shot that year) on December 10. I missed the entire Christmas season. I spent three weeks in bed in a haze, half-asleep and coughing my head off whenever I was awake. I knew that my husband and kids were doing "Christmas stuff" somewhere (the kids went to grandma's house so they wouldn't catch the flu from me), but I really honestly didn't care, I was so sick. I just wanted to either die or get better. (I always get my flu shot now!)
I realize that some non-contagious, non-barfing, non-coughing illnesses allow a child to participate in laid-back family activities, e.g., watching a holiday special on TV. But honestly, if the sick child is around the other kids, he/she will soon be running around and probably make themselves sicker and possibly expose the other kids to the sickness. It's best to just let them rest and get better.
But take the other kids to grandma's (or wherever). They'll resent the sick kid if they have to stay home, and then the sick kid gets upset and feels guilty.
*A strong family doesn't need to be together physically to be together in each other's hearts. * This past weekend, we had a graduation party for my younger daughter (DPT from SLU--yay!). Her sister was far away working and we missed her (I especially missed her, because she's the best cleaner-upper in the country!), but we knew she was thinking of all of us. And when she was finished with her work, she called to see how the party was going.