I'm offering the following as a devil's advocate. Both positions for your kitchen are viable choices with nice reasons to go each way. That's why you need to draw up all possibilities to consider. If the middle is right for you guys, this will end up reinforcing that decision. Versatility and size? That 15x30 room is looking very, very nice as it is, but the far end is prize square footage with all those exterior walls (light/views in up to 3 directions), and right now you plan to actually dine there very little--pretty but underused. If you put the kitchen down there, that addition would be used as intensively as it deserves to be. The living area for furniture placement would be the same, but it would be more strongly defined. Nevertheless the whole should still appear very spacious because it would still be part of a 15x30 room with kitchen on end and still be open to the north, which would extend additional living activities that direction, instead of east. The dining room might well end up used more for various activities in the middle of the house. In considering this alternative layout, how about a pretty door to the outside from a middle/dining room, French perhaps? And for that matter, are you sure you wouldn't have a door directly out from the kitchen? You have an entry in that end that looks as if it would need some reconfiguring too. Would it enter the middle/dining room? Last night I also thought of one other -- possible -- advantage to switching the kitchen and dining room: the step down. This could be a design asset for a dining room, setting it off as special as viewed from the living room. Since you don't plan to eat there a lot, even with young children you could have a nice rug under the table if you wanted it. You'd take that step mostly on the way back to the children's rooms--longer journeys. For the kitchen, you guys'd be making all the many, many little daily journeys between the living room and kitchen on a level floor. Morning sun in kids' hallway? Have sunshine everywhere and you eliminate the pleasure of entering a sunny room. A dim hallway is often a design asset because it makes the rooms opening off it all the more inviting. I can't see what that cabinet in the hall is, but with a little attention to attractiveness and interest, the hall looks pretty good to me. The only way I could imagine to improve it would be to extend it to come back around on itself -- children love to run in circles. :) As it is now, though, the hall enters a sunny middle room in the mornings, setting that room off really nicely, however it's used.

New proposed layout. I did a mock up in in the IKEA home planner but it will most likely use a local cabinet company.

We definitely need more information to make useful suggestions -- right now, any comments are just guesses. We need a fully-measured layout of the space, preferably to-scale as well as a sketch of the entire floor the Kitchen is on. The Featured Answer of the "New to Kitchens? Read Me First!" details the info we need, including several questions to answer. Sample of a fully-measured layout. Note the dimensions include the widths of each wall/window/door/doorway and the distances between each wall/window/door/doorway. Use free downloadable graph paper from the internet. Then draw up the space using Paint, PowerPoint, or other app and label each dimension. The sketch of the entire floor lets us see how the Kitchen relates to the rest of the home. It doesn't have to be to-scale, but it should accurately show how the rooms relate to each other and should include all interior & exterior doors. In addition, it will help us see how traffic flows in, around, and through the Kitchen. Label the front entry and family entry. The family entry is usually a garage or side entry, but it might not be. It's helpful to know which door you use to bring in groceries.

Points in order of priority to me (a home owner, not a designer): The sink and the cooktop are back to back making for choke points and risks of the person at the cooktop tripping over the open dishwasher. In the printed plan with the (presumed) fridge and freezer at the island, any time someone is raiding the fridge you have a choke point. It looks like you have no exterior walls on your kitchen. Getting good ventilation for your cooktop will be an important consideration, which is a challenge on an island because many homeowners don't want a big hood on their island. Also you have the concern about safety with the cooktop in the island and people seated across from it. I would love to have the cabinetry continue on to the table area, it provides extra storage and could act as a buffet. What about putting the microwave down by your snack station and getting the kitchen raiders out of your workspace?