Disagree mildly. When you disagree with someone, you do not pretend to agree for the sake of keeping the peace. You can convey your disagreement mildly by looking away, or grimacing, or raising eyebrows, or shaking your head, or changing the topic of conversation.
Ask for clarification. If someone gives you garbled directions, instructions, or explanations, you can ask that person to restate them more clearly. Rather than going away confused and feeling dumb, you can say, "Your directions were not clear to me. Would you please go over them again?"
Ask why. When you are asked to do something that does not seem reasonable or enjoyable, you can ask, "Why do you want me to do that?"
Express active disagreement. When you disagree with someone and feel sure of your ground, you can express your disagreement by saying things like "I have a different view of that matter. My opinion is. . ." or "I think your opinion leaves out of consideration the following factors. . ."
Speak up for your rights. You do not let others take advantage of you when you feel put upon; you can say no persistently without feeling guilty. You can demand your rights and ask to be treated with fairness and justice. You can say, "I was next in line," or "Excuse me, but you will have to leave as I have another appointment now," or "Please turn down your radio," or "You're half an hour late for our appointment." You can register your complaints firmly without blowing up.
Be persistent. If you have a legitimate complaint, you can continue to restate it despite resistance from the other party until you get satisfaction. You do not allow one or two no's to cause you to give up.
Avoid justifying every opinion. In discussion, if someone continually argues and asks you why, why, why, you can stop the questioning by refusing to go along, or by reflecting it back to the other person. You can state simply, "That's just the way I feel. Those are my values. I don't have to justify everything I say. If justifying is so important to you, you might try justifying why you're disagreeing with me so much."
I have highlighted the ones that I think would serve you well in this situation.
Take care and remember being assertive in not the same as being aggressive.