Your view is lovely. What about white or natural linen sofas, maybe even slip-covered as it'll give a nice casual by-the-water look. I do like the idea of one sofa and 2 smaller/shorter swivel chairs so the view is unobstructed. But I'm not a pro; I'm sure one will chime in.

That rug is not very lake house in appearance. A little formal IMO

Could you do two chairs on each side where a sofa is now, and put a sofa where there chairs are currently? Then 4 chairs might look more balanced.

Another idea. Pull the rug away from tv by about a foot or two and use a cream sectional to keep room feeling airy and to work with rug. Chose one with a low back and place short end under window and view won’t be affected.

In addition to a side table or two, also suggest a coffee table to ground the space and for practical purposes. I think chalk painting the console would be a great idea for a lighter and more casual look

Consider some new accessories and again go light and casual to offset the darkness of rug

I like the rug. While the creamy sofas go with the rug, they don’t work with the chairs.
I would look in the blue range for the new sofas.
The new table should be wood in the same color range as the existing tv console, wood window trim and other wood occasional tables. Wood is always a good look and it doesn’t need to match other existing pieces.
Each seating piece should have a table or surface near it for placing a drink or plate.
I would reduce the number of pillows on the sofas unless the kids like to use them on the floor. The excess pillows can be stored in a nice large sea grass basket for easy access.

I always like some fabric at the windows, even if they are just simple long panels at the sides of the windows to bring a rug color up from the floor.