Nobody can focus on all 3 at once, eyes don't work that way. Front sight is the important one, rear sight and target will (should) always be blurry. Unless you're combat shooting, which is close range and front sight can be blurry, rear isn't used at all might as well leave it at home, and you're still quite capable of accurate shots while being able to focus on the target to make sure it's a gun and not a cell phone in his hand
Red dots are primarily meant for fast acquisition at close range, not precision. I've used them out past 100 and performance is mediocre. Low moa dots are hard to see unless its dim out and high moa cover a lot of target. If you're shooting a 4moa gun + a 4moa dot, the perfect shot can be off by 8 inches at 100 yards. Their best use is for combat shooting as well. Being a single plane sight, you can focus on your target and the dot will overlap your focus.
And if you want to get real trippy, learn to shoot with the entire sight blocked off and both eyes open. It's called an 'occluded eye' sight at that point. Your left eye sees the target, your right eye sees the dot, and your brain overlaps the 2. It takes a bit of practice the first few times.
For your use, I'd suggest a 1-4 scope. Still single plane so you can see clearly, better accuracy than a dot, and you can dial the magnification up/down for your needs. 100 yards (300 really) doesn't need anything more than 4x for big game size targets.
*edit* If you decide to use a dot for hunting, make sure its legal where you are. Some states don't care and you can use mortars and lasers fired from satellites. Others, anything that emits any light is illegal.