Who has first family legal rights over my dad - me or my grandmother?
If, indeed, your father were to be "forced" to sign over any settlement money to his mother, the transfer would be challengeable in court as not being valid because it was done under duress. However, you are much better off dealing with the matter pre-emptively rather than responding to the transfer after it has happened.
If your father is, as you indicate "75% mentally disabled" you may wish to consider applying to court to be designated as either his conservator or his guardian. As his conservator, your duty is to manage his financial affairs. As a guardian, you would also have responsibility over managing matters pertaining to his health care as well. In both instances, you would be required to act in his best interest.
You might also consider discussing with your father, if he is sufficiently competent enough to do so, the possibility of having a trust established into which the settlement money could be placed. If your father agrees, you could be designated as the trustee of the trust to manage the assets on behalf of your father. If your father wishes and there are any trust assets remaining after his death, those assets could be distributed to you or anyone else that your father designates. Ultimately, the choice as to where the assets go is and should be your father's choice so long as he is competent and not unduly influenced by anyone.
Step far away from this situation. Do not be an enabler for this family. Unless your Dad got a settlement that would make Warren Buffett gasp step back, let go and Let God
