I'd call the police and perhaps Children Services to ask what the law is. I think many years ago our city had a law/ordinance in relation to age when a child could be left alone. We went to the home where an 8yo was left at home while mom worked. We talked to both mom and child asking about plans regarding safety. We decided she was safe at home.
I've read of times when the police have been called because multiple children were left alone. Children were taken to a foster home. Parents in court had to agree not to leave them alone before their children were returned. I wasn't involved so I don't know the circumstances. I've read of a couple more.
I suggest the police would not be involved unless someone called to complain. Or if an emergency required their presence.
Just something to consider.
I would not leave a 12 yo in charge of a 2 year old and a 7 yo because watching 2 children can be chaotic especially with a toddler. Consider what would happen if oldest daughter had to deal with both if they don't cooperate or if there is an emergency. You know your children. If you think they'll be safe, if you've discussed what to do in various situations with both the 12 and 7 yo and are satisfied that they are safe, you could try it out.
When I was 11, I watched 2 brothers, 1 and 9 and felt overwhelmed. Because we had a babysitter who left the baby's care up to me, my parents decided since I did all the work, I could be the babysitter. As I recall, I only babysat without an adult a couple of times. After that my mother took the youngest to a neighbor to watch
When I was 12, I babysat several times a couple of kids and it worked out fine. The children were already in bed asleep so I don't remember them.
My daughter, at 12 and with a friend, watched a 2-3 yo and a 9 yo during the summer. So they had 2 babysitters at same time. Mother was a nurse. Father a police officer. Parents of both sets of babysitters and parents of kids could be called at any time. The summer worked out fine. Childrens parents said that ages of 12 were better babysitters than teens.
Both of the successful times, mine and theirs, were with non-family members. That might make a difference.