green option

If you are wanting a 1200mm pivot door, is there even enough room in the dining room to have a good size dining suite and be able to open a 1200mm wide door. Both to me are not suitable entrances. But if these are the only options then I would choose the orange option. Directly into kitchen. This will give privacy to lounge and dining areas. And also easier to position furniture.

You say your front door has to be there. Is there a reason it can't  be on the front of the house in that same corner and swing to where you want to position it now. It would solve the problem of having to walk through the carport and having the entrance looking straight into your kitchen. No doubt you would have to have some sort of porch for aesthetic appeal.

Where is “the front” of the house. Will there be an obvious sight line to the front door. Will people have to search for it?

Certainty  do not want door opening into dining room. No privacy at all.

I would look for a different entrance, you say you want a "special" pivoting door which would be lost on either suggested position. I would also want to run the kitchen bench across to that suggested doorway for a longer bench.

Do you have a whole floorplan to share

Do you need to use the dining room as dining? Or are you prepared to give that space up for entry space. Either way I’d pop some mock ups of furniture into your space and that will indicate where you have room to put the door.

Can you enter from the kitchen wall. Adding a wall at the end of kitchen bench to create a little entry zone?

I'd like to see the whole floorplan too , in fact basically two floorplans -- before extension and after , and any other info like the slope , any existing trees , etc . You say you have settled on a floorplan for the extension , and there is a carport and an alfresco -- the alfresco seems to have quite a few steps , so is it quite a sloping section ? Assuming the 'front' is to the right of your picture ( the fact there is the carport there implies that ) , I am wondering why the rooms shown seem to be quite 'narrow' -- not narrow in themselves , but quite a narrow floorplan if you overlook the carport and alfresco .

Basically , I am second-guessing things , but I'd suggest with more info it would be way easier to make suggestions , not just about the door but the overall design . I have a feeling the door placement is a symptom , not a primary cause of your design queries ?