Here are a couple of web sites that give good information on storing eggs for hatching and about incubating. I know you mentioned a broody hen, but it is still good information.
http://gallus.tamu.edu/Extension publications/b6092.pdf
http://www.ianrpubs.unl.edu/epublic/pages/publicationD.jsp?publicationId=62
You will find a lot of conflicting information on this site as there are few really hard and fast rules. Consider most of the information as guidelines. If you follow them, you will improve your odds of success, but if you don't follow them does not guarantee failure. One very good example is evident here. You are supposed to store eggs for incubation betweem 55 and 65 degrees. Many people here quote success with refrigerated eggs. Personally, I believe them. Many people store eggs for incubation at room temperature, which is above 65 degrees, and have good success. Room temperature is my preferred method. Would we have better success if we stored them at 60 degrees and at the perfect humidity. Probably, but not necessarily.
I'll give you another link about storing eggs for use. You might need to show this to your Mom so she will buy in with what I am going to suggest.
http://www.motherearthnews.com/Sust...ggs-a-Year-or-More-Without-Refrigeration.aspx
Eggs start to lose hatchability after 7 to 10 days of storage. Eggs stored properly for a month may hatch, but the success rate really goes down after about 10 days. This is what I meant about guidelines instead of hard and fast rules. What I'd suggest is setting up a system where you store eggs properly for hatching (for me, room temperature) until you get enough eggs to set under a broody hen. You clearly mark them with the date as you collect them so you know which one is the oldest. Every day, you put the oldest egg in the refrigerator for use as food and keep the newest egg ready to hatch. This way, you are always ready to set good eggs under a broody yet have no wasted eggs.
Depending on your breed of chicken and the individual hen, it may be years, if ever, before she goes broody.
Good luck.