You've hinted at the main concerns with putting poop in a compost pile.
Will putting dog poop in the compost pile spread disease? This could happen either in the act of moving the dog poop, while the dog poop is fresh in the pile, or when you remove and spread the compost. Fresh poop is the most likely source of any disease issues. By using a tool and good hygiene, you should protect yourself from problems at this stage. Arguably, your alternatives are to either leave the poop in the yard or to pick it up and put it in the trash. The former option is probably more of a health hazard and the latter is exactly equivalent. So by putting the dog poop in your compost pile, you're doing something at least as safe and healthy as anything else you could do.
Will having dog poop composting in the pile spread disease? While the dog poop is fresh, if someone or something were to go digging in the pile, they are risking contamination. If you have problems with animals digging through your piles you may be increasing their risk of exposure (an animal may be attracted by kitchen scrapes and inadvertently contact the dog poop). Additionally, an animal digging in the pile may make a mess that you need to clean up. In this event, you now have a second risk of exposure. To mitigate this, I think you would want a well-sealed bin. If you plan to use pallets, you may want something like a chicken-wire barrier to make it more animal-proof. I've seen 4x4 designs that create a very tight box (you do need to allow for air to get in to let the composting process work, though). That might be another option to consider.
Will using the composted dog poop spread disease? If your compost pile reaches high enough temperature for long enough, any likely disease material in it should be destroyed. You can find a number of guides online (https://deepgreenpermaculture.com/diy-instructions/hot-compost-composting-in-18-days/, http://www.soilfoodweb.com/Thermal_Compost.html, etc) for ensuring you get a hot compost pile. These approaches mostly require turning more often than you suggested was your plan but they also produce results fairly quickly so it may still be something you can do. If you can't produce a hot pile, you can substitute a long composting period instead. A common reference for human poop composting is [The Humanure Handbook]. Not exactly the same thing but for the purposes of health concerns much of the same information likely applies. According to this source, two years in a cold pile (never turned) is long enough to destroy any pathogens. If you have room for several separate piles (for example, your new pile that's being added to, your pile from last year, and your pile from the year before) then after a startup period you still have a reasonably continuous supply of finished compost and you don't have the labor of turning (the same resource also suggests you retain more nitrogen in cold piles as compared to hot piles).
Still, not many people recommend using even properly finished (quick & hot or long & cold) human poop on vegetables for human consumption. I'd probably go along with this for dog poop too and stick to grass, shrubs & trees (but I'd be comfortable with trees producing food for human consumption - fruit trees, nut trees, etc - but I wouldn't spread close to harvest time (which you normally wouldn't do anyway)).
As far as grass application goes, though, if the dog poop was scooped from your lawn then there's hardly any risk of further contamination by spreading the result in the same place (ie, it already had fresh poop on it, anything composted at all is going to be less likely to cause problems). So if that's a useful place to spread the material, you may get away with a slightly less complete composting process.
Finally, will putting dog poop in your compost pile inhibit the composting process? This will depend on a lot of variables but I suspect that in most common cases, no. Compare the quantity of dog poop with the quantity of other material. If you have many dogs you might generate enough dog poop to tip the balance. However, a lot of kitchen waste (again, it depends on exactly what you're doing) is pretty low nitrogen (people tend to eat the nitrogen parts). I wouldn't think a little bit of poop will make a noticeable difference. Will it attract flies or other insect pests? Yes, if you don't cover it. But the same is true of your kitchen scrapes so you're probably already covering (or planning to cover) those. If not, plan on it. Chances are, if the poop does bring any excess of nitrogen, it will be balanced out by the brown cover material you put over it.