Child Benefit (Children's Allowance) is not assessable for Rent Supplement (or any Supplementary Welfare Allowance payment), so it must have been cut for another reason.
Other income (part-time work, maintenance, One Parent Family Payment) is assessable when calculating entitlement to Rent Supplement.
If it's been a while (over 12 months) since she claimed Rent Supplement, it might be worth her while applying again, as new rules came in last year, which allow for disregard of some part-time income.