First and foremost, get an attorney to do your will. When you have died, they can file a challenge and you, the best witness, are not around to defend your wishes. The lawyer can do so. Second, the will should clearly state that you are not only disinheriting your children but their descendants as well. In the will itself, you generally should state that it is for reasons which are personal to you. Do not leave $1. People do that for some absurd reason. It does no good and creates unecessary complications. Third, make a written record of why you are disinheritng your children and their descendants. Spare no detail. Fourth, although it is delicate, discuss the matter with friends and make a list of them that can be given to the heirs of your estate. They can be called upon to defend your wishes if your estate is challenged.
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I could not give a better and more complete answer than my respected colleague Tom Begley gave.
The foregoing is not intended to be legal advice upon which you may rely as I have not been retained for this purpose.
Mr. Begley's answer is comprehensive for how to build a strong case to defeat a possible challenge to your will. The only sure-fire way to avoid a will challenge is to have no probate estate to administer. It might be best for you to consult an estate planning attorney about avoiding probate altogether. This was traditionally done by using a revocable living trust, but there are some less costly ways to achieve the same result. Putting payable on death beneficiary designations on your bank and brokerage accounts will ensure that those assets go to the people you DO want to receive them.
I would just add to the good comments already made. First, the general property right under U.S. common law (with few exceptions) is the right to leave your property to whomever you want - i.e., your children do not have the right to inherit your property. As such, there are only limited challenges they can make where a will you execute (leaving them whatever you want or don't want) would be determined invalid (allowing them to inherit your property).
The first is that the will was not executed in accordance with the proper formalities. Because those formalities differ from state to state, I would highly recommend you see an experienced attorney in your state rather than trying to do it alone.
Second, your heirs challenge the will on the grounds that you lacked the sufficient mental capacity to make a valid will. Very generally speaking (again, you should consult a GA attorney for such advice), you only have to able to understand that the will you're signing disposes of your property at death, who the natural objects of your body are, and the general nature and extent of your property. Suffice to say, it is very difficult to successfully challenge a will in those grounds.
Third, an heir may challenge a will on the grounds that it was the product of undue influence - i.e., the person who receives a gift under the will so overpowered your mind that the will was not the product of your own intent. There are a number of factors that give rise to a claim of undue influence, but one of the most pervasive ways to counter such a claim is to have the independent advice of your own attorney in drafting the will without any involvement of a person who may be receiving a gift under the will. (It is extremely difficult for anyone to make a claim that your free will was overpowered by anyone under those circumstances).
Some jurisdictions (I'm not sure if GA is one) also recognize other challenges to a will that is he product of fraud or mistake, and for this reason, I advise clients NOT to put any reason WHY you are disinheriting an heir in the will (e.g., if you were to say in the will that you are not leaving child Xbanyhing because he stole money from you, then child X might be able to challenge the will on the grounds that you were mistaken about the theft, resulting in litigation). Stay away from reciting facts in the will that are disputable or only within the knowledge of you and the other person. More often than not, it's best just to say - "I have Child X, and I am intentionally leaving him nothing."
Finally, if you have a sizable enough estate, you can leave your children a modest gift (I.e., enough that they wouldn't want to lose) and include a no contest clause (I.e., anyone who challenges the will forfeits his or her gift under the will). Again, the scope of enforceability of such clauses depends on state law, so you need to talk to a GA attorney experienced in estates and trusts law.
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