Hi there. I'm sure you will get a lot more help if you can provide some more pictures of the two rooms, and also some info of how you would like to use the space. What does your family like to do, read, watch tv, play games/cards? Do you want a desk space etc?
I see a lot of potential here, just not sure what to suggest.

Here are some more photos of the space. I'm open to any and all ideas on how to use the space. We do already have an office but would be open to a little work area in part of the large room. Hope these help!

Thanks for the extra photos. Having two rooms like this beside each other and so open is a challenge, but here is what I would do. I would have the same window coverings in each room. Add a soft rug in front of the FP. Flank the FP with two comfy chairs, you could probably go with quite large chairs, and put a large circular ottoman in front of them, larger than the one in pic below. Two floor lamps can go behind the chairs.
To update the the bookshelves I have a couple of different suggestions. One is to paint the backs of then a dark gray, like the colour of the sofa. Another would be to add art in front of the middle shelves. Or you could do both. I think that would give a dramatic look. You could put a desk,console or something similar where you beside the doorway where there looks to be a table now.
For the carpeted room, I suggest putting the sofa in front of window, so it's facing FP, and then flanked by two chairs.

You do have a dilemma here. I would suggest treating these two rooms as one with various seating areas. To unify them, install the same hardwood flooring throughout, paint both rooms the same color, and install the same window coverings in both rooms. (Specifics tbd). Then create a seating area in front of the fireplace, and a reading area where the built in shelving is with books. The other room could have the home theater at one end and another seating area with appropriate furnishings and floor and table lamps. The best way to plan your space is to draw it out using the dimensions of your furnishings so that it is designed with full consideration of both proportion and utility. Call or email me if you would like professional help with space planning. It can all be done online.