When mother passes away custody of children

I presume your siblings are minors, correct? And your mother is looking for someone to care for them in the event she passes away while they are minors? If that's the case, the most common, easiest, and most straightforward way to address this is for your mother to create a will and in that will, designate a person or persons (e.g. a married couple, like a sibling and in-law) to be their legal guardian. (Typically, you designate a back-up guardian or two, too, in case the guardian[s] named first cannot or choose to not do this.) In the will, she can also set up a simple "testamentary  trust" that puts the money she is leaving for the minors under the control of a trustee or trustees she names, who can be (and typically are) the guardians, with certain rules over using it: e.g. spend only for support, health care, and education until they are 21, then they get their share of the money. Having a "testamentary trust" (one that only comes into being when the person passes away) prevents minors from getting their hands on money they may not be able to handle. 
The will can be filed in your county, but doesn't have to be: more typically, you give a copy to each guardian and back-up guardian (and trustee, if she chose someone other than the guardian for that role), and to other trusted people, too, like a close friend or sibling or older child (like you). 
You mother legally could draft a will herself, but it's better to let a lawyer do this; the lawyer will also make sure it is signed and witnessed properly (an incorrectly signed or witnessed will is not effective). Many lawyers do simple wills on a very cost effective basis; she can call around and get price quotes. She can also get a power of attorney and living will done at the same time, if she wants.