My mother in law passed away leaving no will, but several properties. The family is arguing about who is entitled to monies gained from the sale of the properties. She had six children, two of whom are deceased. Do the remaining 4 children split four ways or do the heirs of the two deceased children get a portion of the sale as well as the living children.

This will depend on the law of the state where the deceased people lived when they died. In some states all children living or dead would be entitled, in other states only living children would have a claim.

Since without a will, they can not sell the properties without going though probate court anyway, this should be a mute issue, All family members who wish to file a claim do so in court.

This generally depends on what state you are, but in most states, the surviving children, would split the estate.

Since there is no will, an executor MUST be appointed by the probate court. Otherwise the properties can't be sold. The probate judge will advise the executor on the distribution of assets.