OK, here's an endings guide... The endings for Terra are based on her ATTACHMENT and COMPETENCE. Attachment increases when you are kind, consistent, and listen to her (a responsive parent). Competence increases when you teach Terra and require her to do hard things and have high expectations (a demanding parent). Mostly these are affected during Family events each year. So if you want to get Ending #1, you should ignore Terra or yell at her and don't make her do things.
Ending #1 - Bring Back My Baby - low attachment and low competence
Ending #2 - Proving Herself - low attachment and high competence
Ending #3 - Forever My Little Girl - high attachment and low competence
Ending #4 - The Stars are Bright - high attachment and high competence