Deductions & credits

@jjh2006 
Just so as to understand your original and subsequent postings:

• All transaction dates (date of death, date of sale) are current year, Tax Year 2022?
  I note your wording: "Will the distribution from the home sale cash to the four children"  would indicate that the Estate sold the house.
• The house, previously the personal residence of the decedent ( your mother-ion-law), was sold by the Estate's Personal Representative (executor) and the sale was registered in the name of the Estate (or possibly your late mother-in-law's name) and proceeds were received by the Estate?
• If all points are correct, then any gain (or loss) would be reported by the Estate, not the beneficiaries:
• on Form 1041 - not on personal Forms 1040
• The sale would not be considered the sale of a personal residence but instead as an "investment asset" 
• gain or loss would be based on the net proceeds, and on a cost basis including all previous upgrade costs or costs associated directly with the sale
• No exclusion of gain to the Estate would be allowable. 
• Net proceeds distributed would be incorporated into an beneficiary distribution and would be reported on the Form 706 Estate Filing (if necessary, unlikely given amounts) and on Form 1041.
  The gain would be taxed at the Estate level not the individual level. 
• Considerable change to this response would be needed if the beneficiaries each receive a share of ownership of the house itself because the house is not sold by the Estate but instead passes through probate as shares of ownership with the sale to be undertaken by the beneficiaries.

@Anonymous_