I have 3 sisters, 1 half sister and 1 half brother. My father died in 1991 and my mom is 73. There is a house and property. No will. If my mother died how would this be handled? Would the house have to be sold ? If one person refused sale, would it just rot?

Is she married? This does make a difference but since you didn't mention a spouse I'm guessing she didn't marry after your father died. Also, are your half siblings born from your mother or father? If they were born from your mother then they get an equal share upon her death. If they are your half siblings through your father then they are not automatically given a share. So, going with there being six children all of which are her own children, you would each get on sixth of the estate. This does not automatically include bank accounts or insurance policies because they generally have the beneficiaries listed (maybe she listed all of you maybe not).

As for the house, if the six of you could not reach an agreement, then there are a couple other options for handling it. The person that does not want to sell could buy out the ones that do. If that isn't an option either then you might need a lawyer to help go to court to have a judge make the decision.

Of course this is also assuming that there is no debt owed that the estate has to cover before anyone can have a claim to anything.

This web site has a nice "who get's what" chart for Louisiana.
Intestate Succession in Louisiana | Nolo.com

Your mother should write a will - is there a reason she hasn't?
In the will she appoints an executor, often one child, or possibly a lawyer.
If she won't write a will and dies intestate, then the probate court will appoint an executor, and any one of you can apply for the job.

(As for houses rotting because of someone balking - no, the other heirs can force the sale through the courts. Or one or more buy the others out, according to market value based on an official appraisal at time of death.)

Can a will be contested in La? I guess what I am saying is If she did write a will and left everything to one child, is it the final word? Basically, I don't want any of the property, I just don't want to deal with the drama once she is gone. My siblings don't get along well and I see a war coming when she passes. No, she never remarried. My half sister is hers biologically, my half brother is my deceased father's son. The property is paid for and she has no debt. Having her write a will is like talking to a wall, she says we can deal with it once she is gone. The problem is I don't want to deal with it. I want her to get it settled before she passes because I know I will be stuck in the middle of hell.

A will can be contested anywhere. It doesn't mean the court will agree. Contesting a will is expensive, so not worth it unless the estate is pretty big.
Do your best to reason with her for your sake, for all your sake.
Her best bet is to just put it in the hands of a lawyer, and let it be boilerplate, in that all six of you get equal shares. It is standard for the house to be sold and the proceeds divided when there are that many heirs, unless one can clearly afford to buy the others out, but that part doesn't go in the will and is not her concern.
If the estate is divided equally I can't see a lawyer willing to take on a case of one sibling wanting a bigger share, regardless of who is your mother's child and who is your father's and who is both.

Some states do not all a child to be completely disinherited.

As Joy said a will can be contested anywhere. Where the suit has merit or not is another question. A lawyer can make a will that will withstand assault.