Because you are living in Kansas since 2010, you would have to file in Kansas, not NY.
Kansas is an Equitable Distribution state meaning that generally any property (including the house and 401K) acquired during the marriage with funds earned during the marriage (excludes funds received as an inheritance or gift from a parent) are considered Marital Property, regardless of in whose name the property is held and will be divided approximately 50 -50, with the court retaining discretion to make a different division based on extenuating circumstances.
Good Luck,
Leonard Weiner, Esq./Divorce Solutions
212-370-1660