I keep a couple of acoustics handy around my house as well for similar reasons. I have one on a guitar stand beside my desk in my home office so while I am waiting on a computer program to open or waiting on a download I can grab it and play a bit.
I keep another one on a stand next to the sofa and I will pick it up when I am relaxing in the living room.
I have found that a guitar that is comfortable to hold, comfortable to play and sounds nice will be picked up and played more often than one that is too cumbersome, too uncomfortable to play or sounds dead.
I know what you mean about the Rover - it's not comfortable to hold and because you have to fight to keep it in playing position - it is not comfortable to play either.
A parlour style guitar as Droog mentioned might fit the bill because they are generally smaller and comfortable to hold and sound nice. Keep in mind a typical parlour guitar will join the body at the 12th fret and the bridge is closer to the bout putting the soundhole in a different position. But a decent well made parlour style guitar will usually run you over $200.00
Some of the smaller 3/4 size guitars made by Martin and Taylor are quite comfortable to play and sound really nice. The smaller guitars made by Yamaha and Fender will not sound very inspiring. But again, the 3/4 size guitars that sound nice will run you over $300.00 US.
I have occasionally run across some really good sounding Chinese made guitars that you might find used for a really nice price. I have one made by Great Divide that I purchased new for under $150 and it literally is one of the best sounding acoustics I own. It's the one sitting beside me as I type this. It has a concert style 000 body so it's comfortable.
I like to look at used guitars in the local guitar shops because sometimes you find a really nice guitar that is heavily discounted because it might have some minor damage. I picked up a nice Guild Jumbo once that had a hairline crack in the back but it sounds great for a $150 guitar. I've had it for about 7 years and the crack has not changed and it still sounds great. I picked up a Gibson acoustic with a cracked neck and had my luthier glue and clamp it back together - then sold it for double what I paid to another musician friend.
If you have little ones running around and you find a guitar you like to play, you are going to want to keep it safe most of the time. I recommend a wall hanger positioned high enough so that the kids can't reach it on run into it.

You can buy one similar to this for around $10.00 US.

Or you can make one similar to this one that is in my office at home. YouTube videos abound to describe various ways to make wall hangers for guitars for under $5.00.
Suspending a guitar by the headstock exerts no pressure on the neck so it will not warp the neck the way leaning it against a wall would. The only thing to be aware of for any acoustic guitar that is stored on a stand or hanger in a room - is that air that is too dry (as you might find in winter heating season) or too damp (as might be found in some basements or cellars) can have an adverse affect on the guitar and cause shrinking or swelling of the wood.
The ideal humidity range for an acoustic guitar is between 45 and 55 percent relative humidity - but anywhere between 40-60 percent should be fine. An inexpensive digital hygrometer to keep tabs on the humidity level would be good to have in the room your guitar lives in. The one pictured below costs less than $10.00 US.
I wish you luck in your search and much enjoyment from whatever instrument you select.