Does Lan care about your children? Of course, and I find the South American culture to value children more than in North America, or at least coddle them more, so you will find the staff of Lan quite considerate of your kids.

You state the rules are that Base Plus fares can preselect seats, and not Base fares. If this is true, you will have a hard time finding a Lan employee who will break the rules, for you or anyone. If you care about your children, and you obviously do, then why not buy a Base Plus fare? Problem solved. Why do you think that because you have kids Lan staff should threaten their jobs by breaking the publicized and clear rules?

All that aside, if you check in right at the 48 hour mark and get to the airport early you'll likely get seats togther. If not, I have found people on the Lan planes to be more than accomodating in swiching seats, especially to have children beside their parents because they care about children... and I've seen FAs assisting in this.