I am not sure I understand what you mean to say in the first sentence. It definitely has prevented me from working towards leadership positions but would I explain this in the "extra essay" or somewhere else?
Is caring for your siblings something you do because you want to ----- or do you perform this role so a parent can work? The essence of the question is can you really qualify this as a job? Is the family counting on you for this function? If you were off doing other things -- what would happen? Would a parent have to quit their job to then watch the children? Would some unsafe situation result with twin 5yr olds being left at home as latch key kids after they walk home alone from the bus stop? Details matter and they will help you tell this story to others. Remember, the admissions board and the nominations board do not know you or your circumstances unless you tell them. If caring for siblings has impacted your ability to do other things, share that with them. Highlight how this role has helped you mature and has better prepared you for USMMA.
If this is a job (paid or not), it can go on the student resume. Expect the topic to come up in your nomination board interview. Everyone's situation is different, but here are a few that I have heard over the years:
"Candidate XYZ, I see you have a job here for 20 hours a week. That's a lot for someone of your age. What are your responsibilities?"
Answer 1: "Well, I try to help out around the house and keep my little brothers out of my mom's hair after school."
Answer 2: "Yes Sir! I live with a single parent, and he/she needs to work past 3pm when my siblings get out from school. I need to care for my two brothers by picking them up from school, and taking care of them until my parent gets home. To do this, I have had to step back from some of the activities I was doing previously and I was able to get a work release from High School to leave early enough to pick them up at school. I generally get them started on their homework, clean and start dinner. Once my parent gets home, I can start on my homework. Teamwork makes the "team" work! At least it works for our family."
Answer 3: "Yes Sir! Things are a little financially tough for us right now and my parents both work very long hours to keep up with the bills. We made a choice as a family to have me care for my siblings after school so that we would not need to spend money on after school care for the two of them. I know that I have not been able to participate in a lot of things outside of school and caring for siblings, but I am trying to demonstrate maturity, character, and leadership in different ways and I hope that comes across to you though my actions."
As a USAFA ALO, I dig for these kinds of details because typically, a candidate who is serving an important role like this for a family will be the last to talk about it. It's life and it isn't glamorous. Most candidates in this situation feel that it is not as important as other leadership roles like the ones some of their peers are doing -- but I would disagree. We need to convey to all parties involved why there may be perceived gaps in the resume. A resume bullet like this can actually do a lot of good for the candidate and really speaks positively to maturity and character.