The second one faces the window and the TV, I would go with that one.

Are those drawings to scale? If so, both layouts look crowded. This first one crowds the kitchen stools and the second crowds the door to the lanai. Have you considered putting the chairs across from the sectional? Or trying smaller chairs or just one chair or a larger sectional?

In the first one, there doesn't seem to be enough room between the island seating and the two chairs. The second one would I think be better, but I'd shift the sectional a bit towards the island, leaving more room for the chairs near the patio door. The two chairs might shift a bit toward tv to allow better access to the patio door.

Option two 🤎🤍🤎🤍

Are you commited to a sectional? Your space seems smallish (when considering traffic patterns and doorways) for a big piece of furniture like that. If you didn’t have that hallway door near bathroom #2, it would lessen the traffic through there.

A sofa plus chairs would be much more flexible and as noted is less bulky, but lets you shrink or expand the grouping ( by how you place chairs, tables, ottomans) over time as you get more familiar with your traffic patterns and how you like the sight lines. You can create an “ L “ on either end with a chair or make a “ C”.
If you already know your family’s relaxing style is perfectly suited to make best use of the sectional , then that may be different but I think they’re often sold on basis of static “ looks” more than comfort and functionality. I think they underestimate the benefits of side tables for drinks and such - though you can use C tables for some of that- and having place for more than one person to put up their feet. Hence another reason to understand how much space you have to allow for things like that as well as pathways.
Just something to think about.

Thank you, everyone! The drawings are not to scale. I'm attaching a layout with dimensions. The overall area is about 20'x17' and area where the sofa would go has a coffer ceiling about 12'x16' (red rectangle). I'm also attaching the dimensions of the furniture that I would like to put in there. One of my main goals is to have plenty of seating space since this is the family room and there is no other siting area in the house (i.e., there's no other living room/tv room). Of course, I would like plenty of seating space without compromising flow and without making it crowded.

Thank you, again!

How many people use the room regularly? How many when you have guests? Are you wedded to the idea of a sectional? Sofa and chairs, with an ottoman when you want to put your feet up, give you more seating.

My living/tv room is quite small and I really wanted a sectional like yours for the chaise. However, all of them stuck out just enough to encroach on a doorway. I ended up using a long four seater sofa with recliners on both ends. It's worked out great for us.

Room looks pretty dark for me, so I would not block door to lanai.