Should I complain about my HOD (2nd Placement ITT)

I've spoken about this before but I'm at the end of my teather. Today, the HOD sets a really complex computing task for year 7s which means they download the file, then they upload the file and the program is done for them.

When I did it his way, I lost 10 mins trying to get students to do that. I realized a better way would be to live code it with them following me and then going round to help them complete the rest themselves (scaffolding).

He storms into my lesson and in front of the kids says what are you doing why you have adapted it. I want you to follow the scheme of work consistently (btw, the scheme of work consists of a lesson title - no I'm not kidding).

He pulled me and the another trainee in and both of us explained that he uploads the lesson plan and slides a day before or at worst on the morning of the lesson. How can we do long-term planning in a situation like that? I am someone who likes to make sure I plan in advance to save time. He arrogantly said we are free to be flexible - but then he wants us to stay consistently with the SOW (the lesson titles in a spreadsheet with no medium term plan and lesson objectives).

Should I tell my training provider? I only have 4 days left, but I really want to get this off my chest because I can feel myself bubbling with anger at being scapegoated for someone's bumbling incompetence? The trainees who we swapped with warned us this is how it is with the HOD, I think some kind of record needs to be kept because this is not only impacting on the teachers' mental health, but more importantly, the kids are getting a crap computer science education.