Is it permissible to donate money from my mother's bank account, or must I have my own bank account, or should I collect the money at home and then take it to the charity?

Performing charity every day is permissible; indeed, its doer is rewarded. This is based on the Almighty’s saying: "Who is it that would loan Allah a goodly loan so He may multiply it for him many times over?" And based on the saying of the Prophet, peace and blessings be upon him: "Every joint of the people must pay a daily charity as long as the sun rises." It does not matter that the account belongs to your mother, as long as you are giving charity from your own money.