As with most questions, the answer is "it depends."
If the child is named as a beneficiary of the account or it is a joint account with right of survivorship, then "no," other children do not have any right to the contents of the account upon the mother's death. Everything in the account would belong to the sibling on the account.
If, on the other hand, the child is simply a signatory on the account and no beneficiary is named, the mother is still the sole owner of the account & her estate would own it upon her death. In that case, the contents of the account at the time of her death would be split amongst all of her heirs in the same manner as the rest of her estate.
(If the account is recent, it is highly likely that there is a beneficiary. Most financial institutions will no longer open accounts without named beneficiaries.
----The advice given here is not intended to, and does not, establish an attorney-client relationship. Also, the advice given is general, based solely on the facts stated in the question. Other facts, not listed here, as well as the contents of any documentation involved in your case may substantially affect your rights/obligations. The only way to know for sure is to schedule and appointment with an attorney to discuss your case in detail.----