You seem to be acting emotionally, rather than rationally to this situation. Take a step back and analyse the situation.
Deep breath.
Do you think you are frustrated and giving yourself a hard time over the student not complying with you, or is this part of a bigger issue? Do you think you are transferring the blame to your colleague?
My analysis of this situation is that you and this other teacher perceive your roles differently in the school. She may see herself as part of a team working towards a common goal, whereas you think it is important to have sole authority over the students you teach.
Have you considered that her aim was not to undermine you, but show the student a united front? From her perspective, if she had walked away and ignored the students behaviour, she would have been condoning it.
Every teacher has a different personality and communication style. You don’t need to compete with each other. It’s trial and error finding out what works for you and you won’t always get it right. Teaching also involves learning. You can learn from your colleagues, you can learn through professional development and you can learn through reflective practice.
Part of being a teacher is about developing your practice and looking at how you can improve. No teacher handles each and every situation perfectly, people are only human. Cut yourself some slack here.
This is an opportunity for you to reflect on what the factors were at play in this interaction, how the student responded and what you would do differently next time.
If you want some tips, ask your school if there are opportunities for training courses relating to classroom management and behaviour managment.
In the meantime, there are free courses for teachers available online through the open university- I’ll find the link for you.