9/28/14:

Ambrosia is fitting in well.  She is quite comfortable and vocal with her demands for affection.

We are still learning new things about her.  She enjoys sleeping with the kids,.. and attacking toes.  I had wondered who kept spilling her water... until Austin saw her dipping her paw into the water and then licking it.  Strange cat actually thinks she likes the dogs.  She does not run from them, but sniffs them,... and licks them.  I still supervise their interactions.  Last night, for the first time, we witnessed her running full throttle through the house like a possessed animal, then she decided to attack my shoe.  Considering she likes the smells of people and dogs, she has terrible taste for a cat.  She did explore playing the piano just today, so she may have musical talent.  She has not yet been introduced to Boogar, but knowing both of their odd personalities, we all agree that they will get along fine.  We all figure that since we're all so weird, we were destined to have another weird cat as well. 
The only potential question we had was whether she'd had a litter of kittens in the past.  She appears to have "used nipples."  That would explain her tolerance for the kids and the dog as well. 
No deal-breakers thus far.  Like I said,  she's fitting in just fine.