Does anyone have good literature or information on the hukm of bowing down and doing sajdah in front of the teacher in martial arts?
Some Muslims do it saying that it depends on your intentions. This new Muslim mother doesn't want her children to do anything wrong.
بِسْمِ اللهِ الرَّحْمنِ الرَّحِيْم
In the name of Allah, the Most Gracious, the Most Merciful
The works of the jurists suggest that bowing down when doing karate is a Makruh (disliked) act and should be abstained from. Although if one bow down to the sensei without the intention of worship, but merely as a gesture of respect or greeting, one will not become a Kaafir.
Only Allah knows best
Written by Maulana Irfan Ali
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 Fatawaa Hindiyah vol 4 page 481