Who is the legal heir of a married women who dies without a Will leaving a husband, son, and brother?

When a person dies without leaving a Will, they are said to have died "intestate". In such a case, state law will determine how a deceased person's estate is distributed. In LA, inheritance rights depend on whether the property in question is separate or community property.

Generally speaking, community property is property acquired during the course of a marriage. Community property includes the earnings of both spouses during the marriage, the house and household goods they buy, and property given to them jointly. While they are married, community property belongs equally to both the husband and the wife. When one of the spouses dies, the surviving spouse receives ownership of thier 1/2 of the community property. The other 1/2 belongs to the deceased spouse's estate. If the deceased spouse has died without leaving a Will, their children inherit 1/2 of the community; however, but the surviving spouse retains a "usufruct" over the property. This means that the widow/widower can use and enjoy the benefits of the property until their death or remarriage.

Separate property is property that belongs to one spouse exclusively. This includes property acquired before the marriage, or property given to or inherited by one spouse only. When a person who has not made a Will dies and leaves separate property, their children inherit it in equal shares.

As for any inheritance by an adopted child, they are treated the same as a biological child.  If there has been no formal adoption than typically they would not inherit. And, as long as the deceased leaves surviving children, their siblings (brothers/sisters) have no inheritance rights.

Since LA estate/probate law is different than most other states; you really should consult an probate attorney to more fully discuss your rights.

What you have actually presented is oftentimes a law school conundrum and depending on a huge number of factors (like capacity of husband if he has a will, whether the adoption was legal or not, whether case in law in your state states it doesn't matter or does matter if the son has to be legally adopted and other factors), the likelihood the property is the husband's and the son's now is slight.  If she owned the property prior to their marriage and it was in her name only, you have to look to see if she ever transferred title to include both of them on the home.  If not, did husband contribute to household expenses, including any existing mortgages or taxes?

If it is her separate property and in no way community property, it goes to her brother.  Otherwise, it goes to her spouse.  It probably will never go to the step son unless there is some sort of adoption that is legally binding or would be recognized by the probate code.