Howdy. Im a law enforcement officer (Game Warden) in Colorado, and I've had experience with about every kind of gun made by man. There is not a perfect all-around gun for every use. If you are talking about dogs/coyotes, you dont need anything too big- and ammo is cheaper for smaller calibers. You wife will want something smaller also. As far as deer hunting, you need to check you state laws. Many (most) states have minimum calibers for deer. Some states require shotguns, not rifles. So you need to answer those questions first. Putting the deer hunting questin aside, I would look at a Ruger Ranch rifle, .223 caliber. It's small, light, sturdy, dependable and the ammo is cheap. It's a bit small for deer, and not legal for big game in Colorado, but it's a great little gun for everything else. Once you know what is legal in yoru area for deer, then you know what you need for that use. I would bet you a T Bone steak that if you want to do everything you stated, you will end up buying two guns. Also, dont discount the 12 gauge slug for deer, depending on what kind of country you live in.
Best to you.
