Besides, empathy, accurate information. If as you mention, this was their 47th puker of the day, then the CM should have been well versed in what solutions to offer the Mom, including the nearest companion restroom (something they should know anyway, in order to assist guests with disabilities), or offer like someone said the Baby Center...and I would through in First Aid. Both places would likely have better "clean up" supplies, than your normal bathroom.
OP, I am sorry you had to experience such an uncomfortable and trying situation. But your post highlights something that I've been feeling for a long time, that CM's are less capable of handling things that are "out of the ordinary." If it's not easy, and fun, many want to do as least as they can, get rid of you and let it be someone else's problem. But other than lip service to old ideals, they aren't expected to, aren't trained to, might even get in trouble because it interfered with their expected job duties. Turnover is pretty high, and many don't spend any free time exploring the parks, so many CM's never gain any sort of mastery to help them be of superior assistance to a guest beyond their immediate job area.
For any business, they are measured, not in when situations are simple and easily accomplished, but how well they deal with the "curveballs" of something going wrong. You, unfortunately got a rude awakening on where Disney falls on the spectrum, currently, and not coasting on their reputation.