Those are teenagers, they should be big enough to be interviewed on their own. Of course every parent has their reason, maybe they have doubts about the Bishops' methods, the children feel uncomfortable, etc.
Lets look at the reasons why a parent would want to be in an interview with their Teenage kids.
1. They don't trust the Bishop.
2. They don't trust their kids.
If the Bishop's integrity is questioned, then there is an issue that needs to be addressed by a higher authority (Stake president).
If a parent doesn't trust their kids,a bishop's interview is not the place for a parent to try to find out what a kid's issues are. That should be discussed in their own interview.
An interview with the Bishop should be a place where a baptized member should be able to talk about their worthiness. If there are any problems with worthiness, then that should be between the Lord, His servant and the individual. A parent should find other avenues to find out what the child is having problems with.
Would I as a teenager been willing to confess a sin in front of my parent in a worthiness interview? Maybe not. But I do not understand why a Parent would want to be in the interview with their teenage children unless they have some trust issues themselves.
So to answer this I would say "yes a parent could go into a Bishop interview with their teenage children", but then I would ask "why would you"?
Name: MiaMaid
Comments: For me the first question needs to be asked here: Why does the bishop need to see my kids one on one? Also, isn't someone supposed to be around because of policy, like in the next room?