You did not mention what state you are from but generally adoptive children are treated the same as natural born children for inheritance purposes.  You need to be concerned with many things here and it may be hard to give any real advice.  

First, are you over the age of 18?  I am assuming so.  Your Mother is not dead.  Incapacitated but not dead.  So the assets of your parents are still both your parents.  What you really have here are two parents who are incapacitated for different reasons.  And both need to have a legal representative appointed on their behalf who would be able to make the medical, financial and legal decisions on their behalf.  If you are an adult you would be the best candidate to do so.  As for your Father in New York you would bring an action under the Mental Hygiene Law to have him declared incompetent and you appointed as his guardian.  Same for your Mother but for different reasons.  You would then be given the power under the law to administer to the properties in any legal way.  There appears to be no other person to validly challenge you on this.  You are an only child. 

Seek legal help as soon as you can.  If your relatives are really the type you say every moment counts.  Good luck.