First of all I want to express a heartfelt thank you for each of you for taking time to share your expertise with a stranger. There are many valid points in your answers.
To Pmacduff: Unfortunately there is enough income tax owed to absorb 75% of the QDRO because no taxes were paid out of her disability or alimony. Just knowing this makes me feel a little angry, but she has had no extra cash for luxuries because her medication has taken every dime.
ESOP Guy, she has no family and as I said, she is a recluse, in part due to a movement disorder with symptoms similar to Tourette's. The situation is urgent, but you are wise to suggest I seek assistance from a pro before the distribution. I tried Belgararth's idea (your kindness was more than I expected) and called a trusted charitable organization who found an expert volunteer willing to come to our home to help with the taxes. And last, but most definitely not least, QDROphile, your brilliant suggestion is the best way to protect the portion of the account she cannot put toward her debt; she will be in danger of homelessness if she is not receiving adequate care.
I was pleasantly surprised to find that everyone who contributed here withheld judgment on the issue and gave well-considered advice. Thank you all so much for that. Best regards.