Soundly advice. By selling your house you're stepping out of the housing market.
As someone who is not in the housing market (and paying $560 per week in rent) it is demoralising to realise that a mortgage would be more affordable but we are stuck in a catch-22 (have to rent, can't save the deposit because we rent, but could afford to pay a mortgage off).
With regards to (some of) the other things.... (please don't bite my head off) .... I think he's right.
Clearly you both worked hard to get a home to raise your children in. I wouldn't want to lose it either.
Kudos to him for taking on university (I don't know what he's studying but his start salary on completing a degree will be a lot higher than without a degree - you can get to the same salary but it takes a lot longer) and working part-time. It would be hard work studying during the day and working at night.
I understand that he doesn't want you to work full-time. You will have two children to look after and the childcare costs could outweight the income you might receive from a full-time position. Not to mention that you will have two extra days to get up early and get everyone off to work/uni/daycare. Then there's the coming home thing....cooking dinner, day to day jobs. Is it worth the extra stress?
I used to take Mondays off. I loved Monday's everyone was at school/work and I could catch up on cleaning, baking, shopping and me time.
Men like to provide. Well, at least my DH does. And, FWIW I like (I mean really truly like) ironing his shirts, preparing a fabulous dinner, tidying the house and "looking after" him and the kids. He does the "blokey" jobs - garbage, cars, lawns, spider removal, gardening... he also cooks me breakfast every single morning and masages my tired feet at the end of the day.
It sounds like you are feeling a little overwhelmed with the money.
When money gets me down I sit down and work out what I need to pay out that payday. Quite often the outgoing is more than the incoming. I prioritise things: roof (rent), heating (electricity), food (groceries), transport (petrol/car). Things always work out - sometimes I think I should have been an accountant!
By all means make contact with your local centrelink office and request an interview. You might be surprised by what you are entitled to.
Your DH sounds a lot like mine. While I'm stewing and fretting over things he is calmly sorting it out in his head. I'm the emotional one and he's the logical one.
Take care hun and just don't make any rash decisions (such as selling up) before seeking further advice.