I would suggest not removing the load-bearing wall. I've been told it's fine to do before but the walls nearby and the ceiling just end up with major cracks.

Re: the load bearing wall issue - perhaps you can incorporate some pillars as part of your island and take up a lot of the load that way>>>

Consider taking the wall out btw the foyer and living and the kitchen and dining room, if possible. Work with an architect, who will likely be able to refer you to a structural engineer, which is critical to your process. The load bearing aspect, with respect to the wall placement is one concern, but also certain walls serve as shear walls for lateral bracing, if you live in a high wind and/or high seismic area. I am not a fan of seeing a kitchen when I come in the front door--I feel it should be left, at a minimum, partially concealed by leaving the center wall in common with the living. This project is becoming more complex than when you posted and I responded earlier. While your design team is at it, have them take a look at the wall which creates a hall next to the family room. That room, as much as any space, will function better as a larger room than it will as a room which is 11' wide. I wish you well in your pursuits.

We have a formal dining room table that needs to stay but we can afford to shrink the width of the dining room to (at the smallest) 11 feet wide. I don't mind/like the idea of pillars in the island and we will need to have at least one post in the space to support the weight of the new header/beam. Right now I have two ideas in mind one is the pictures below and the second is bumping out/moving the existing wall between the living room/kitchen 2.5 feet closer to the front of the house and putting an island in the kitchen. The only difference is I prefer something a little more open to keep and eye on my daughter and see out the front windows.

Agree with having the entire kitchen occupying the existing nook and opening up to the dining room.