My mother-in-law's ankles are black and blue and swollen, what can be done?

Can your brother-in-law visit in person to talk to everyone and anyone at the nursing home? Is there a way to get the name/phone number of the doctor who visits your MIL at the nursing home? Give him a call and request an exam.
I would also contact the social worker at the nursing home and ask how to file a complaint with the state and other boards that might oversee nursing homes in the area. Sounds like you are going to have to keep calling the nursing home everyday if necessary.

I hope all goes well.

This is a medical problem that most likely has to do with circulation. Is your MIL diabetic? Does she have congestive heart failure? Does she get any exercise? These three questions came to my mind. If you MIL has not been seen by a cardiologist, she needs to see one. If she is diabetic, she may need to add a medication to help her get rid of the fluids. Doctors could check the peripheral veins and arteries for sign of disease. Peripheral vascular disease can be painful, so it isn't something to ignore.

It could be so many things, but tests will need to be run to see what it is. Since the older son is 70, I am assuming your MIL is probably 90 or more. Is she under palliative care? How advanced is the dementia? These questions are important in understanding why the NH may not being aggressively treating symptoms. Please let us know a little more about the situation.