How about volunteering for a campaign or in a rep’s office? Or working on some local advocacy project? I have no idea what the student iniative is, but there’s benefit in working on established teams, learning from adults and fitting in. I know you’re busy with siblings, but you’re asking about some of the most competitive colleges.
A lot of poli sci kids don’t get this more direct experience, it would be noticed. And you do need to be careful about how you note time babysitting- you don’t want the impression that you can’t leave home, no one could take care of the other kids. IF there is a next-age sib who could take over some babysitting, maybe he/she could help now.