So sad to hear about the poor dead hoglets.
It seems best, at this stage to leave the other nest alone. If there is a mother (potentially a different one) in there with youngsters it would not be good to risk disturbing her in case she deserted them. Being packed solid with leaves sounds reminiscent of a hibernating nest, although not at this time of year. I suppose it’s possible the hog could have used more of a hibernaculum type structure to insulate from the hot weather we’ve been having – but that is complete speculation. The ideal thing would be to aim a camera at the hog house entrance, but I’m guessing you don’t have one? But I wouldn’t check the nest, unless, i.e. you saw a lot of flies going in there.
Bird food is not really good for hogs – it tends to be things like sunflower hearts/peanuts, etc. which have an imbalance of phosphorous and calcium which can cause, particularly hoglets, to grown in a deformed fashion. So bird food is best cleared up so that hogs don’t eat too much of it. Would it be possible for you to make a feeding box (which your dog couldn’t access), where you could offer the hogs some more suitable food, i.e. cat/dog/meaty hog food or cat/kitten biscuits?
It’s important to leave water available for hogs, all day, every day – especially in dry weather. It is often easier for them to find wild food than to find natural water sources. Wide but shallow plant saucers are ideal – not so deep that a hoglet could get into trouble.
Although, I appreciate, you are a bit concerned about your dog eating the dog poos. I sympathise. We once had a dog which took to eating from a nearby dung heap and then sicking it up in the house! But it sounds as if the hogs have voted with their feet and like your garden! Hopefully hog poos are fairly easy to clean up. They are often situated where the hogs tend to congregate – like feeding areas.
Good luck and happy hog watching!