Its kinda hard to answer that question. Generally speaking, if you suffer a loss of employment you can apply for Jobseekers Benefit (subject to PRSI cons) for the days you are not working. So if your employer reduced your hours, then its possible. However, if you reduce your working hours yourself then you haven't suffered a loss. Also to qualify for JB you should be available and genuinely seeking work on the days you are not working.
RE JA for your husband. That depends how much you will be earning for the 2 days you will be working in the prospective new job. You require that figure to work out the means assessed.
If you have dependent children FIS might be an option if you will be working over 19 hours per week. In your current position unless you have 3 plus children, you will be above the income threshold for FIS on your current income.
A