My personal favorite is option 1, here drawn a bit more clearly:
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A small pantry directly accessible from the kitchen, with a small window in the west or no window at all. Here I’m almost for no window, because west or south-facing windows can warm up the pantry. Windowless with motion sensor lighting and controlled residential ventilation – that should keep the temperature in check. Of course, a pantry isn’t ideally oriented this way, but it helps. Then, a freezer can be placed there, saving space in the kitchen. Simple and inexpensive shelves on the wall can easily store pasta, flour, and the like. There is also enough space for various beverage crates and cartons. Not to be underestimated with four people.
If there is a window, then it must have automatically controlled shading, otherwise the pantry will overheat.
The utility room will take the rest of the kitchen space saved. I would put all technical appliances in the west and use the front of the utility room for storage space. For things you need repeatedly: vacuum cleaner, all cleaning supplies, kids’ rubber boots, etc. Otherwise place the space-saving staircase as centrally as possible in the house. The advantage is that you can stand upright in the attic when you come up.
The guest WC should be widened a bit and fitted with a proper washbasin, and the door should open into the WC. A small recess for the entrance to the utility room makes the coat area more open. Hooks can be installed on the wall there to quickly hang a frequently used jacket; above that a shelf for motorcycle helmets, hats, etc. Coats, hats, gloves go into the closet. Shoes can also simply be taken off in this niche and left there or you can put a small low shoe rack there. With four people, a lot of shoes quickly accumulate and show me the kids who always tidy theirs up nicely... they don’t exist. So at least I get the kids to take off shoes in the niche and then leave them lying there, but not in the hallway where everyone trips over them.
I would reconsider the door to the living area. From experience (we had it that way in the previous apartment), I say: it is always open. Possibly choose an opening so that you first try it without a door and if it is missing, a door can be installed later without much trouble.
Now I hope for a convincing report from haydee and that your wife can be convinced of an open kitchen.
Then, as drawn above, I would widen the island a little and let it extend into the living/dining area.
This provides additional storage space (narrow base cabinets or open shelves) that can be accessed from the front (e.g. for table linens, napkins, paperwork you need in the living room, etc.). Then, of course, the small cabinet drawn there is omitted. Good argument for the dear wife: with full shopping bags you immediately have a great place to set them down!
From the kitchen, a normal terrace door, which can also be wider (we have one 120cm wide), so you can easily pass through with a tray, for example. A sliding door is not necessary, but I would definitely keep the access to the terrace.
The short wall that is now on the south wall between the kitchen and dining area obviously has to go.
Again: instead of the two windows, install one large sliding door. That makes the room livable and open – even if it’s just a green wall there (be glad that there is a green wall, we look at the neighbor...).
Then plan the kitchen. Usually, the stove/ceramic cooktop/induction is planned on the island. I wouldn’t do that – you rarely stand at the stove, usually you are prepping at the board and are at the sink. If technically possible, I would therefore put the sink on the island (not centered, as that ruins workspace, more in the third toward the wall) and the stove on the line along the wall. But that is just my advice. Observe your kitchen routines consciously over the next few days as you use it – that will give insight into how you should plan your new kitchen.
With the kitchen planned this way, your wife is somewhat separated but has full view of the living and dining area (and thus the kids). Here I would even do without a second dining place in the kitchen (also without the bar solution, which would only be in the way here). Coffee standing up works fine at the island and otherwise the table is nice and close anyway.