The rules you give are quite useful. Thank you.
One thing that I would add is that I can remember easier if I think in terms of who is actually entering. If the Subject is entering, then we use être, but if the "entering" is being done by someone/something other than the Subject, then we use avoir.
Mes filles sont entrées en CP cette année. -> Mes filles
Nous avons entré les informations dans le programme. -> les informations
This works in other cases where we need to decide between avoir and être. (or where the sentence seems to indicate that the action is not done by the sentence subject)