when you're cooking you'd need room to move around ..or pop your sink on your island and the stove on bench the rangehood doesn't need to go against the wall can go up to the ceiling and be vented out.. I wouldn't put the stove in the corner..better to have in the middle so you've got bench space on each side to pop your dishes and colanders etc whilst you're cooking

I understand the beam being installed when you did your earlier extension as that was an external wall, that's why I have suggested keeping part of the wall next to the island which was also an external wall, to support this, I will check this in the drawing to ensure it lines up for you. By opening up this wall as much as possible you are allowing more light back into the house The cost of running plumbing across I think is negative/comparable to moving the plumbing for the re positioned laundry and kitchen and removing any load bearing walls. Storage in the new kitchen is a big 2900 x 900 island of drawers for easy access, I have added a wall oven but that could become a 600 pantry with drawers in the lower part with a shelf above for small appliances. The wall with the TV could be a wall of narrow built in storage to be used in any way you need. This floor plan gives better flow between kitchen/family.dining/alfresco and better for unloading the car with the driveway running down beside the kitchen and verandah

still not sure about the measurements...if the entry hall and stairs are 2850 wide and the dining and living are the same width then the kitchen must be longer than 5570...sorry to be so pedantic but all suggestions have to begin with accurate idea of existing spaces...but keeping the kitchen in the original space there should be enough room for a modest WIP, stacked WO and MW. 1m wide fridge space, 90cm cooktop and/or recycle old stove , rangehood, sink, and DW with more useable counters and storage and consider combination of wall cabinets and/or open shelves across the sink wall and in front of the windows long term when kids are older i would close the opening between living and dining and create an opening between dining and playroom to make a combined family, dining, kitchen area with a separate media living room

As you appear to use the back living as the dining, I would have a break in that side of kitchen for ease of access. I would close up the current exit opposite the bathroom. I would move fridge across the room and move pantry next to it. Remove the current pantry walls and right angle the cabinets, on both sides, instead of angled. Move oven to near the cooktop. Maybe underbench oven. Microwave and appliances along those benches with overhead cupboards. The angled walls that close off the front living may be load bearing. So you would need to get that checked out before thinking of knocking them down for stools to be placed there. You also have so many appliances on the benches. You need somewhere to put those when not in use. If you open the walls, then you will lose that storage area.