In your relationship, it'll be a negotiation, at the start, and also throughout. Daddys or doms get to propose things, and so should littles/subs - depending on the dynamic. People can agree to things, try them out, and if something doesn't feel right, then it gets re-negotiated.
Also, i'm just starting to learn more about ddlg, but some people regress, get pulled into little space and can be more vulnerable there emotionally. As that happens, different rules might apply (i.e., no sexual interaction of any kind in little space, or only loving ... or... whatever you guys agree to.
A dom should definatly check in w their little or sub, and if the little uses a safeword, or checked in with and gives a color (green is okay, yellow - close to the line, red - stop everything), that's how when someone might say no - we can still check in w them to make sure that they aren't just playing and that they are mentally and emotionally okay.
It's okay to nudge boundaries, but you kept being uncomfortable, and he should've backed off and talked about it, rather than telling you 'this is how it's going to be', and 'thank me when i'm abusing you - generally, it's okay because i say it is'.
It's not. you are in a relationship, and that person as a daddy is supposed to be more protective and nurturing of you than in some other relationships. You get to negotiate everything, and whatever you don't accept, they can't automatically do unless it's something you want to try once to see how it is.
Also, emotional care and especially aftercare is important. They don't own you and you have to submit to them or their will, you give yourself (your time, energy, etc) to them willingly, and they are supposed to take care of you.
What i read in your post wasn't loving, or protective, or within the bounds of the conversation. It's okay to roleplay and also push boundaries a little, but he didn't respect your feeling. And you mentioning this was causing you anxiety was a huge red flag of no that he ignored.
He isn't fit to be your daddy or anyone's until he learns that lesson.
Best wishes. You deserve better. Run away from them. And find someone who respects your boundaries.