The entire reason that people create Wills, is so they can designate who they give things to. Your mother could have left absolutely everything to charity and removed you all from her Will. So the answer is yes, she could have taken you both out of her Will and left everything to her adopted child. You could possibly find out about her Will and any probate proceedings by checking with the Probate court. Documents regarding your mother's estate will have to be filed with the Probate court. There are also documents you can file if you want to try to challenge her Will. But there is no guarantee that a challenge will work to get you anything. It all depends on how detailed she made her Will in excluding you. If her Will specifically excludes you, that will be more difficult to challenge than if she just doesn't mention you. If she just doesn't mention you, they may say that she just forgot to put you in her Will and you might succeed in a challenge. Probate court should be your first stop to check for her Will, or if you have any clue which attorney drafted the Will, that's another good place to start.
If competent at the time of executing her will, she could leave everything to charity, her favorite friend, an individual relative or the person who mows her neighbor's yard.
If she wasn't competent, then her estate would pass under the laws of intestate succession. Not an easy thing to prove, and not something you'd want to try going at on your own.
Attorneys Pate and Foster have provided you with solid answers. One further point: there may be nothing that passed by the terms of her will. That is, if she had a fully funded revocable trust or had every asset titled with a beneficiary designation, these assets will pass outside of probate (that is, outside the terms of a will).
This information is presented as a public service. It should not be construed to be formal legal advice nor considered to be the formation of a lawyer/client relationship. I am licensed in Connecticut and New York and my answers are based upon the law in those jurisdictions. My answer to any specific question would likely be different if I were to review a client's file and have the opportunity to interview the client. Accordingly, I strongly urge you to retain an attorney in your jurisdiction with respect to any legal matter.
Your questions have been fully addressed by my colleagues:
check with the local probate court to review her file (if the will was probated, the content of the will, etc). That is of course assuming she did not have a trust and all her assets passed into the trust.
And yes, she can write any one into or out of her will.
This answer is provided for informational purposes only and it is not intended as legal advice. Additionally, this answer does not create an attorney-client relationship. If you wish to obtain legal advice specific to your case, please consult with a local attorney