There are a few potential options.
1) You can approach the HoD Director and just tell them your issue. Do not be argumentative - tell them that you have been working really hard and that you and your friend are feeling like your efforts are being constantly belittled. You need to give and take - give them an out for their attitude (no matter how bullsh!t it is) - "I understand tech is high stress from all sides, we have put a lot of effort in, and I know you and your directoral team have an artistic vision that you are invested in, but we would appreciate a bit more courtesy - in some instances we have followed the brief - and then been called out because of reconsidered artistic decisions. We want this show to work and help achieve your vision, so would really appreciate it if instead of calling us out, you could just articulate the changes you wish to have made politely and acknowledge that this is a change to the brief". If that does not appear to work, proceed to #2.
2) Resign. Do it politely. Take the high ground. After the rehearsals, approach the directorial team "It appears that you are not satisfied with our services and it appears we have reached an impass, with regret I am afraid we need to part ways." - This potentially brings you back to point #1 with some negotiation.
3) Everyone has a boss. The HoD has a boss. Perhaps talk to that person. I don't really suggest it, because either they will be bought into line (and then potentially harbour dislike after being talked to by their boss) or they won't.
4) Pull them up. When they say something rude and disrespectful to you, "Can I have a moment over here" and take them over to a private area and call them out; If they start down the "Well this is how it is in the real world" - hit back with "And in the real world I would have called you out in public instead of being respectful and talking to you in private." Could result in reverting to #2.
Unfortunately, as with the real world - when your boss is being a jerk and the relationship has devolved to the point that you cannot work with them any longer, there is little you can do except stick with it or walk away. But never storm off, never shout "I quit!" and storm out. ALWAYS take the high road, always be respectful. Because if you arc up and start shouting and screaming, you will be the one that is painted in a poor light. If you do it respectfully, even if they start to badmouth you in front of the ensemble, it is them that look like the arseholes.