I am XXX, friend of the family (kindergarden teacher of the child, child's aunt etc). I have known the mother and the child for XXX years. During that time we spend (how much, how often) times together. These encounters allowed me to observe the interactions between the mother and the child.
I am here to testify that the mother is capable to provide excellent care for the child (factor 1), or the mother had excellent relationship with the child (factor 2).
First, the mother cares about the child very deeply. For example, on such and such date, she did this and that etc.
Second, the child loves to spend time with her mother. For example, on such and such date, the child said this and that. etc.
...
My observations above made me to conclude that it is in the child's best interest to grant the mother full custody of the child.
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This is how you prove a case. Cold hard facts. No crying nor drama. Now do your homework, find your witnesses.