I would remove the paneling, change the double hung windows in the dining room to the muntin style windows on the other wall and possibly use tall glass doors for the built-in unit. It would be helpful to see the exterior of your home.

Take it down, especially if you are planning to return it to a Tudor style bungalow. You have beautiful furnishings!

I say take it down in the living room, but keep it in the dining room. It would look better painted, and perhaps modify it like these examples.

I would take it down under the window only in dining room

As an ex-Brit: Gotta say (tongue in cheek!!!) Thank you for saying Tudor-style rather than Tudor (which would suggest/mean your home was built between 1485 and 1603!!!) ;-)

Traditionally, Tudor-style walls were plain, white plaster, so the paneling isn't in keeping with the style.

LOVE the door.

I would keep it but paint it and the trim in white

I'd take down everything except maybe the cabinet area in the dining room. See how you like it with all the rest removed. Not feeling the love? Paint it & see...still no love? Rip it off. Doesn't cost you anything except a gallon of paint & a little time to see if ya like it.

OMG...that little screen door is as cute as can be!!! :0)

Paint it

I'm mostly with bungalowmo. Remove the panelling in the dining room where it looks a bit odd because it's not on all the walls and is not in keeping with the style of the house. Keep the cabinet bit, however, and assess how it looks - it is potentially a good feature. In the living room, I would paint it to blend with the wall and see how it looks. You may want to add a little extra 'architectural detail' to it if you decide to paint as by painting it you will remove the decorative effect of the timber, which is the reason it was originally installed. Alternatively, you could carpet the dining room and either leave the timber or paint it because the main problem with the room is that there is just so much timber everywhere and not a lot else happening to excite your eye. For the same reasons, the living room needs a much larger rug, some more furniture and a few well chosen artworks and the panelling won't be such a visual issue. Good luck.

Just came upon this thread and wondered what you decided to do....and what the original fireplace behind the paneling looks like (assuming you removed it!)?