Push your dining table up by the built in seating leaving room for a small sofa and possibly one modern feature chair. At meal times, they can sit at the built in seating as it will make them higher up at the table. Define the 'lounge' area with a rug. Keep the children's area over by the shelving and have a small low desk area included in the shelving system for them to sit at which would remove the need for kids table and chairs.

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Fantastic idea for seating, been beautifully designed.

I prefer accent chairs with arms. You could certainly add another one if you wanted. As you have quite a lot of upholstery I would use something different like rattan or wood.