I agree with most PPs - reassess your budget and see where you can tighten or be creative with ways to earn extra money. We pay our cleaner $80 for 2-3hrs of work each fortnight, if you could get even 1 or 2 cleaning jobs like that you could easily work around your DPs shifts. Also look into work from home option like data entry or even home-based call centre work. It might take time to find something that works around your DPs changing shifts but it's worth keeping an eye out.
I'd also seriously consider DPs work options. It sounds like he's not earning much and might be paid the same amount doing a basic 9-5 job or retail work. That would then give you a lot more work options.
And I really encourage you to give up smoking. If you're struggling that badly I just can't understand spending money on cigarettes. At least cut right back. Think about how much quicker the debt would go down if your cigarette money went on that instead.
I get nothing from the government except CCR so I can't comment on CL benefits, I have no idea how they work and doubt we'd be entitled to anything.
Good luck, I hope you find another source of income so you can feel like you're getting somewhere.