In considering your application for guardianship, the court will take into account your age. 19 is very young to shoulder such a burden, but it has happened before.
Another option would be for you/your mother to petition the court that you or someone else be appointed conservator of your sister's property. Generally, a guardian is charge with the physical care of the ward, while a conservator bears the responsibility of handling the ward's property.
You and your mother can always make a joint petition for either of these things. The court will decide the matter based on the best interests of the child (your sister).
If you need an attorney and cannot afford one, check with your state bar association. They may have a volunteer lawyer program where attorneys will take your case at a reduced rate or without chargin you a fee.
It is possible that the temporary guardianship your mother gave your cousin has expired or that it was done without court involvement, in which case it would be relatively easy to file a guardianship petition with your mother's assent.
If the guardianship actually went to court and has not expired, you or your mother will have to file a petition to remove that guardian and assign you.
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Since he is over age 14, your brother can "nominate" the person who he wants to serve as his Guardian. Under the Massachusetts Probate Code, your mother has a say in designating the Guardian for your brother and sister.
MCLE has posted a book online that covers the Probate Code sections:
But, you are at a disadvantage if you try to figure out by yourself how and where to file the petitions for Guardianship of your brother and sister. Take a look at the petition form you have to file, and you can see how complicated things will become when you consider the relationships involved here, and the notice requirements. An objective professional can work with you to give the Petition the best chance for getting approval.
You didn't mention whether the state's child protection agency is involved yet. But if the situation escalates, that might happen. Hiring an experienced guardianship attorney to help you is a first step toward stabilizing your family's situation.
A Petitioner's checklist is posted at:
I practice in Hampden County, so I don't have information on legal resources serving Boston and Suffolk County where you are located. But those resources are there. Contact the Massachusetts Bar Association, the Massachusetts Guardianship Association, and the Massachusetts Trial Court Law Library. Their contact information is online, and they can direct you to the legal services that would be best suited to serve you.
-John L. Roberts
Estate Planning, Elder Law, Probate and Disability Law