You might try reading this article. It gives good information about how to store eggs for incubation.
Texas A&M Incubation site
http://gallus.tamu.edu/library/extpublications/b6092.pdf
These recommendations are general guidelines, targets to shoot for, not absolute unbending laws of nature. These guidelines do not guarantee absolute perfect success if you follow them exactly, nor do they guarantee total failure if you violate one. Just follow them the best you reasonably can. The more you violate them, the more you reduce your odds of total success, but many of us don't do things exactly right and still have pretty good success.
On the temperature, for example. I don't even remember the "ideal" temperature range for storage given in that article, but I don't have a place that meets that. I store them on my kitchen counter with the AC for the house set in the mid 70's. I just had a broody hatch 11 out of 11 eggs stored that way. Some people in hot climates may store the hatching eggs in a refrigerator if they don't have a better place. Different refrigerators are set to different temperatures. That's why they have an adjustable thermostat in them. Some spots in the refrigerator may be warmer than other spots so storing them in a refrigerator means different things to different people. The longer they are stored in the refrigerator and the colder they are stored, the less likely they are to get a great hatch rate. But many people get really good hatch rates storing eggs in the refrigerator. Know the target to shoot for, then just do the best you reasonably can.
I don't fully understand what is going on with the hen that is pecking holes in the eggs, but it may be years or never before any of your hens go broody. Not all hens go broody, even if they are breeds that are known to often go broody. They go broody when the hormones kick in. Those hormones may never kick in for your hens.