Dear Alex,
I am happy to offer you my design idea for the space in which you hope to create a home for you and your family. This is a large and beautiful space with so much potential, and I enjoyed designing it.
If you look at the proposed layout, you will find that I have dedicated about 3/4 of the available space to your primary residence. The remainder is designed as a separate studio, which (when needed) can be easily incorporated into your primary residence. One thing you will note is that I did not alter any of the load-bearing walls, which, as you know, will help make this proposal budget-friendly. Similarly, all three baths and the studio kitchen are adjacent, so your plumbing needs (and planned budget) will be fairly contained.
One clear challenge of the project is the large central area, which, if not designed properly, stands the risk of being devoid of natural light. I decided to have that space remain large and open, accommodating a spacious, chef-style kitchen with a large island, a large dining area, and the entrance. I suspect that this space will get some natural light during all hours of the day because it communicates to the bright living room and the small hallway to the children's quarters, which are on the opposite parts of the building. However, special attention will need to be paid to the lighting of this area, for which I propose some large, contemporary and interesting pendant lights. I find that large mirrors, which would reflect both the natural and "artificial" lighting, always help in such places. The living room is large and bright, with plenty of comfortable seating for some quality time with the whole family. Your master bedroom is similarly spacious, with a lot of natural light and an adjoining master bath. There is a second large bath, immediately adjacent to the entrance, which is always convenient. I put the children's rooms where your prior entrance was. One of the rooms will have an access to the terrace.
The studio itself has a large bath, and a good size kitchen with an eat-in area (bar on the right wall). The path through the kitchen/dining area leads to a large room with a ton of natural light. This room has a sleeping area and a seating/lounging area.
As you had requested, the design style is modern and simple, but warm - I propose light, hardwood floors, and simple, light colors. This works especially well when there are areas challenged by sub-optimal natural light. You will see that most items I propose are in white and light gray, with some espresso/black items for some contrast and definition. I also propose a few brightly colored items (in this case, bright yellow), which freshens up a room.
As for the furniture suggestions, the PDF file contains a detailed list. On the left you will find some excellent pieces. Some of them might be on the more expensive side, so in the right column I suggest some equally fitting, but more "wallet-friendly" options :)
I hope you will enjoy it!
:)