I can only comment about the cowhide rug idea as that's my area of expertise. Cowhide are still going very strong as a design trend, they haven't been overdone in my opinion. Also cowhide rugs break all the normal rules of standard rugs because they are an organic shape. So they visually take up more room than they physically occupy. So you don't need a cowhide rug to be as large as a wool rug. They also look better on a 45 degree angle to furniture and it is OK for one or several legs to go underneath furniture as this can anchor a group of furniture. For how to clean a cowhide rug there is some great info on my website plus a video that is really interesting.

Lower right. You don't neccessarily have to have all 4 feet of sofa on the rug, but you should have at least the front 2. You'tt probably want a more durable, washable rug because of it's location at the door. Best length would have to be judged based on door location and some sensible distance from TV -your 10 - 20 cm? Out of curiousity, what is the white box in the upper right of the room? Is it movable? If it is, it looks like your sofa could go on that wall, and a light chair (or 2) where sofa currently is. Then the area rug would be centred on the sofa, the chair legs might not be on it, and rug would be away from the patio door. Is that any better?

First ,is removing excess furniture an option? Second, why bar fridge in the dining area, that really ruins the look. Seems that you can not move dining table closer to the kitchen because you have light pendant above the table, so can you move piano where your black couch is and couch on the other side of the room instead of creamy colour sofa . I notice the luck of coffee tables and side tables,that's probably why you like to sit around dining table, it is not visitors friendly and doesn't encourage conversation or interaction. I will come back to it have to study photos more. Are the arm chain the other room similar colour to the couch in the dining area?

You’re right in that it’s quite skinny now. The floor plan I uploaded is actually the original, since then whoever renovated removed the return on the bench and added an island instead. I’ve uploaded a photo of that below (don’t mind the mess :)). We’re struggling to envision how we can modernise the space without shoe horning something in that isn’t quite right, i.e. I’d really love a big island beach but can’t see how we can achieve that without moving the structural wall. As with most families, we spend a lot of time in the kitchen - it’s the busiest part of the house so we’d like it to be modern but also functional with plenty of space for the kids. We see the lounge room as more of a serene, quiet space for us to relax at the end of the day when the kids are in bed. I’ve included more photos of how we currently have the place set up. We’re also going to replace all flooring with vinyl planks (kids and inside dogs don’t mix well with real timber floors).