A will is a legal declaration by which a person, the testator, names one or more persons to manage his estate and provides for the transfer of assets at death. In my state, the testator can decide who gets what. Check with your lawyer again to make sure you understand what you were told about this adult child situation.
I see from your profile that you are from AZ. You really should get a second opinion. I am a Florida attorney and when a parent wishes to exclude a grown child from their will, you just specifically add an exclusion clause removing them from receiving assets. States vary in their constitutions as to requirements in preparing Wills. Your attorney should have explained this to you. IF it is a matter of leaving them $1.00 in order to accomplish this, then you need to find out if this can be done. Contact the Arizona Bar and Lawyer Referral in your area and they should be able to put you in touch with an attorney who handles estate document preparations.
I am an Arizona attorney. You can exclude children as long as you are competant to write a will. You may have been given bad advice or misunderstood. You cannot prevent the "left out" children from _contesting_ the will, but you can make it morelikely that they will lose by having your doctor perform a competancy exam around the same time as you prepare and sign the will.