The only way to work on pitch is... to work on pitch. That is to say focus on simple diatonic exercises with some vocalization and move them chromatically up and down the piano to the ends of your range.
Different syllables will feel different and require some adjustment of the mouth to get good resonance. Interestingly enough there is a single mouth shape that helps with this for all syllables (according to my vocal coach). So you wind up learning to adjust the tongue and face muscles to generate an 'ee' or an 'ah' when your mouth is shaped like an 'oh'.
If you have a vocal coach and your pitch issues are being 'ignored' as you say then you may want to just ask for help and see how that goes. Otherwise find another coach.
A little over a year is not long. I've been at it for 3 years or more and still drift out of tune. One thing that helped me in the beginning was using an electronic chromatic tuner like the Korg AT12. It will measure your pitch when you sing into the mic and it can also be set to a drone so you can sing with it and match the notes.
Based on listening to you sample you provided my opinion is that your voice was not supported by your diaphragm more so than you were out of tune. Lacking support can cause intonation to falter. Having proper support from the diaphragm make intonation more stable.
Just keep at it and you will get better, but again talk to your coach and stress that you feel like you need help with this issue.