K.B.
J.:
I would start with the Salt Lake Tribune/The Deseret News/Indeed.com/KSL.com and possibly Craig's list to get a general idea about "work from home" opportunities. LDS Employment/Provident living might also be a good resource. It also depends on the skills you already have that are applicable to the job and what you enjoy...
However, if there is no compromising leaving home and your children to do some type of work, then it might be really difficult. No matter what you do, I am sure there will be some kind of training that you would need to go to or be involved with that would not necessarily be done at home...
I know of employers that have employees telecommute from home, but most of them are phone/call center related-NOT an option for you. Plus, they often offer it to those with seniority.
You could have a business with Mary Kay or other cosmetics lines, Maleleuca, USANA etc. but they all will require some cost upfront to get started. Then, you have to sell, deliver product, attend classes etc.
All the best in finding the right opportunity for you...