This answer is based on a number of factors. How old is the child with bipolar disorder, and how old are the other children? How symptomatic is the child with bipolar? And what other special needs do the other children have?
In younger families, managing the intense mood swings and tantrums of a child with bipolar disorder can turn into a full-time job for both parents (assuming we’re even talking about a two parent household). Frequent visits to doctors and therapists and regular meetings with teachers can shift much of the focus from other children.
For children who have severe mood episodes as well as significant management and behavior problems, finding a therapeutic afterschool program can free up three or more afternoons a week. Some insurance companies will reimburse for these, especially if the child has had prior inpatient hospitalizations. If a school system, through their evaluation of the child, believes a therapeutic program is needed, it’s possible that they will pick up the tab.
Enlisting the regular aid of another adult, either a family member, friend, or paid assistant, can also diminish the overall parenting burden. In some instances a grandparent who has a good emotional connection with the child with bipolar disorder may be able to provide regular respite through overnight, or weekend, away visits.
Finally, in some states, and in extreme circumstances, state agencies may be able to provide parenting assistance through programs offered through the agency that oversees children (in some states this will be Department of Children and Families, in others it will fall under Health and Human Services, Public Health, Mental Health, etc.)