You want to till the hydrated lime into the soil. If you get your lime at a farm store, it will be safe to use around animals. There are different types of hydrated lime, and yes some can be harmful. That is why when you goto buy it tell them you are using it around live stock.
Secondly it doesn't take alot. Just make sure to work it in the soil. And only add some when it starts to smell.
Yes DE is expensive, bc it is made for use in the food industry. You can get none food grade for less money. But alot of people use too much of it. DE contain silica. If you breath in too much silica it can do damage to your lungs. Food grade DE contains less silica but can be just as harmful if you use too much and don't get it tilled into the soil you are working with or bedding.
It scares me how people rub DE all over everything etc. If you aren't wearing gloves DE can actually make tiny cuts in your hands or if you are breathing in the dust that is bad too. ALWAYS WEAR A MASK when working with DE and/or Lime.
Good Luck
Nick