I also agree with Kim. Tell EVERYONE that you're looking for a job. And do write up a resume and apply, apply, apply. You don't have to organize your whole resume around a time line. There is a form of resume called a "skills resume". List true, verifiable skills especially if you did volunteer work or coached teams (cheerleading!). Write a cover letter that you can customize with every application but DO emphasize that you were a stay-at-home mom for a while and just recently decided to return to the workforce full time (I think that helped me land the job at Dillards - which, BTW, does come with benefits.)
Have someone review your resume. Actually, have more than one person review it. Feel free to modify your resume to fit the job for which you're applying (highlighting certain skills over others - not lying, of course.) DO use keywords, especially if you see certain skills listed in the job posting. Many resumes, especially the on-line ones, are scanned by a computer program first. If those key words aren't there on your application, your application won't be seen by human eyes. DO fill out the entire application AND attach your resume AND cover letter for every single job to which you apply.
Most applications are on-line now. I think in hubby's job search he turned in only one physical paper application. I never wrote a paper application until I actually got the job and had to fill one out for legal reasons.
Your state unemployment office will probably have an on-line job board that is available for anyone to use.
DO tell your current part-time employer that you're looking to increase your hours. Perhaps you can work part-time in the kitchen and part-time in their office or something else.
Don't worry about the temp agencies having more work than they are able to handle. Most of the people on unemployment don't want a long-term temp assignment because it goofs up their unemployment eligibility. Since you're already working part-time, do tell the temp agency that you're willing to take a part-time assignment if it meshes with your current job.
If your hubby does lose his job, immediately go to H&W and apply for benefits (TANF, food stamps). You might not immediately qualify but you'll at least be educated on when benefits will kick in and your children can get on Medicaid or medical subsidy. Your hubby won't qualify for unemployment because he was fired for cause.
BTW, did you know he was drinking during the day?