I hope I am wrong....but the girl is taking advantage of your care and concern for animals....I always like to describe the blatantly obvious.
If it were me, I would simply tell this individual that crunch time has arrived and if she is not capable of taking the cats that you can no longer keep them and have found a suitable home for them. I suppose the downside of this is she might either take them and try and find another individual to do what you have generously already done or subject the cats to an unfitting life. Since she has already played upon your sense of fairness and concern for living animals by stating she would just have to take them to a shelter...it doesn't sound like she gives a **** in the first place UNLESS it's completely convenient for her. So, force her hand again and hopefully she will say the same thing regarding the shelter and then you can simply tell her you have found a wonderful "shelter" already for them and proceed to place them with the potentially interested party.