If he 'can't manage' invoicing, looking for work etc, then that's a bit pathetic, it drives me straight up the wall when creative people act like they should just be able to waft around doing their special snowflake thing and not deal with the nuts and bolts. So that's one thing. If he wants to do this thing, then he needs to do it properly, at least, and I don't think that's unreasonable to expect.
He isn't making enough money to support himself, let alone children, so he should be 'paying' in kind, the way any SAHP does, in terms of housework, childcare etc. Do you feel he does enough in this area to make up for the financial support you're giving him? Would the things he does have to be outsourced (childcare/cleaning etc) if he was working more, or would you be able to do more of them?
As for you wanting more.... I'm trying to look at this fairly. I don't think it's fair to expect a partner to provide a level of income that you yourself can't or won't provide, basically. If you want to be rich and he doesn't, then it might have to be you who makes you rich!
On the other hand, it's not fair if he's not working as hard as you in general - so, taking childcare and household into account as well as employment.
Is the job/hobby one of those things where he needs a 'big break' or is it really just a question of him not working hard enough? I think it's all very well to 'not be materialistic' but we're not talking someone who's happy earning min wage, we're talking someone who isn't bringing in enough money to survive on, and I'm not sure that's ok unless both partners are happy with it - which you're not!
Are you directly financing his hobby/job? Ie paying for things he needs for it? If so then maybe that's a place to start making cutbacks.
Alternatively, if you're paying for childcare, that seems a bit silly, and maybe he could take that on instead. I know you don't want to encourage him to work LESS, but perhaps if you make the position a bit clearer - he is, in effect, a SAHP after all - then he might discover that he WOULD like a bit of extra money and maybe would be willing to earn it?