I'd say apply for JSA immediately, the payment will be small but atleast she will be able to do some courses as if you were in receipt of FIS she would not have the option of doing a course to prepare for work.
If she did do a course there may be an increase in payment from the reduced JSA payment that she will get.
You can always apply for FIS as well as her JSA, though the payment could be just €20 per week, but still something. If you are in receipt of FIS the family will also get the back to school clothing and footwear allowance when the children are of school going age.
There will a major drop in income for the time being but as you work out a new budget and pool your resources things will get better.