I feel your pain, but there are some tactics you can employ and if you divide it up between the six of you, it shouldn't feel like so much of a burden. One or two of you can set up a time to go to the gym with her. Water aerobics is wonderful for older ladies and if you (or whoever is with her) is a little more extroverted, you can wind up making some friends.
Does she play bridge? Or something of the like? One of you can volunteer to get involved in a bridge club with her. Minimal commitment for the child, and again, she could wind up making friends that she pursues away from her child.
Anything that you can coax an ounce of interest out of her, you or one of your siblings needs to pounce on and look for social opportunities for her, take her by the hand, and help her navigate the scary waters of socializing. She probably has quite a few issues about her failed marriage and is very nervous about trying to put herself out there as a solo entity. If she's open to therapy, that would be great, but something tells me you're going to have to be a bit more subversive to get her to make personal progress.
Think of it like this: She has six children that she once took by the hand as you neared the playground, nervous about whether the other children would accept you and include you in their games. Now, she feels the same and needs her children to return the favor. With any luck, it won't be long before she's on the teeter totter with her new friends and not all up in your business all the time.
Good luck.