How to deal with a family member who manipulates and bullies Grandpa to now make him leave her large amounts of cash?

If your grandfather is no longer legally competent, you need to get this diagnosed so that any new gifts or bequests are not valid. Informing cousin of this might avoid problems. If he is still legally competent (and incompetent is not the same as mild dementia or aging memory loss), he needs help to overcome the bullying. It might be best to go with your grandfather to a lawyer who works with elderly people. Talk grandfather through what he wants to do (and the lawyer needs to be willing to go on record that you have not pressured him in the meeting). Then get the lawyer to draw up any relevant documents to put into effect what he really wants. Make sure that you also get any other paperwork in place - POA, will, HIPPA etc. Get them signed ASAP.

If he is of sound mind he has the legal right to do with his money and will as he pleases.

You need to get control of Grandpa’s finances. If he is of sound mind, have him give you Power of Attorney. If he’s not of sound mind, apply for guardianship. That way, you will be in control of his finances and cousin will be left high and dry.