It isn't unlikely that the mother wanted to take her with instead of... throwing her to the nearly literal wolves, but even so without the court being able to verify the veracity of who wrote said note then its basically worthless
Even if the note from the mother is legit, the father who is not getting deported and fighting for the kid's return absolutely should have had a chance to state his position before a judge.
"Something's wrong! Murder isn't working and that's all we're good at." ~Futurama