John, First, I'm so sorry to hear about your mother.
To the business at hand, do you have a copy of the document that gave your mother power of attorney for your grandmother? Usually these will designate and alternate, in case the first cannot serve. If this designates a person other than you, then that person may act for your grandmother. You may be able to challenge that, as her next-of-kin, but you'll need to speak to an attorney likely to get the full picture.
Speaking of attorneys, you likely need to talk to one about settling your mother's estate. Even if she had no real property, you'll need help to get the bank accounts or car title transferred to you (assuming your mom didn't have a will and wasn't married, you're her sole heir.)
A great first step may be to talk to a low-cost or free attorney at one of the Neighborhood Legal Clinics. Because your issue involves the care of an elder, you may wish to attend the Elder Law clinic. There are also general law clinics held in various parts of King County. Check it out here:
http://www.kcba.org/legalhelp/nlc/clients.aspx
If you live outside of King County, check with your county's bar association to see if they offer low-cost legal help. Simply search "(your county) bar association" to find the general number and give them a call.
Another thing you can do is to talk to the ombudsman at your grandmother's care home. It may be that, as her only living relative, you can make all of the decisions necessary on her behalf without a power of attorney.
Good luck and, again, sorry for your loss.