What are guidelines to allow my husband and I to claim his elderly mother as a dependent on our taxes?

IRS.gov has a simple worksheet you can use to determine if she can be claimed on your taxes as a dependent. You can go to the site irs.gov and look for that, or you can use this to go directly to it. https://www.irs.gov/uac/who-can-i-claim-as-a-dependent?_ga=1.27155583.314868011.1475602305 Tax laws can be pretty tricky so I don't want to start guessing when it's simpler for you to check the site.

I ask if the elder's estate is in a trust because the tax implications will be different.

apply for the medicaid before you claim her as dependant.
As dependant total household income inc yours.Is used If she is living in assisted then apply for medicaid and longterm care usually for persons over 60 but there are exemptions. Does she have medicare. Does she qualify for skilled care. Unfortunately assisted living unassisted living is more than most of populations Soc Sec and definately more than SSI. contact your Local Elder Affairs and Soc Sec volunteers they will help with any programs avail. for extra funds. In FL it is Sunshine Volunteers.
Any money you pay for her keep will be considered a gifted and or income.AND can keep her from getting benefits.
She needs Lonterm care if she is Parkinsons disabled. Try the foundation maybe a volunteer advocate can help guide you.
I also suggest eldercare lawyer to help set things up for her to qualify for medicaid. Some are volunteers some are income scaled. call Public defender office for info re pro bono or scaled legal assistance available in your area or Courthouse.
Go to Parkinsons foundation see if anyone in area can help you with list where to start. Longtermcare usually has deadline of Nov. for applications usually for 60 and over designed for persons with medicare. But, not necessarily true. first word you say when looking for help should be disabled dx Parkinson. ok .Best wishes.

Is the estate in a trust?

Where I live, Medicaid only takes over after two years of private pay concerning AL. And a Medicaid room has tobe available.

Apply for Medicaid, that will help with some of the expenses as well.

If you are paying more than 50% of her expenses you should be able to claim her on your 1040.