Final answer:
The client's statement about feeling overwhelmed with juggling time for their mother and children indicates role conflict, as it reflects the difficult balance between caregiving and parental responsibilities.
Step-by-step explanation:
Role conflict occurs when an individual is confronted with competing demands from different roles they occupy, which can be stressful to manage. The statement that indicates the client is experiencing role conflict is: I feel overwhelmed with not having enough time for my mom as well as my children. This statement exemplifies the tension between the role of being a caregiver for an aging parent and that of a parent to their own children, which commonly arises when individuals must prioritize different responsibilities that conflict with one another.