It can't hurt to get more involved, and certainly I'd choose 2 good leadership oriented activities than 5 non-leadership ones.
However, if you are caring for a disabled mother, thats a reasonable excuse. I wouldn't use work as an excuse because, frankly, there are people who work in IB who end up doing some pretty stellar activities... so it's not really going to convince anyone.
However, explaining that you would like to be more involved but "the unpredictable nature of my schedule due to my mother's illness, unfortunately precludes me from doing so" should be a reasonable explanation.
Two words of warning: Bringing up your mother, although entirely legitimate, risks sounding a bit like "take pity on me". Just be careful not to overdo it. Mention it, and move on - explaining how you plan to take a more active role in school (a natural question of course would be - if you cant now, how could you then? )
Personally... If i were you: I'd go get a leadership role with one or two of your activities (pick one youve been involved in a long time ideally). If you can't do that, I'd fall back to the mother excuse - but I'd use that as a backup, not as my primary explanation.