Your mother will not be able to qualify for an H – 4 dependent visa based on the fact that you and your brother have been issued H – 1B visas. Only spouses and minor children of H-1B visa holders will be able to qualify for the H – 4 status.
Absolute No... Only your spouse and children under 21 may be issued H-4. Consult with an immigration attorney. There may be other options available to your mom - depending on your situation. All the best!
For truly dependent parents it is sometimes possible to obtain a B-2 visa for them to accompany you. Consult with an experienced immigration attorney for more information.