I didn't mean to undermine what you do - and obviously, also understand why you wouldn't want to explain exactly what your life's like in public so to speak in case you're identified. However, I stand by what I said about having an in depth talk, the pair of you, about what it is you expect/need from each other in order to keep your family fully functioning - and hopefully reasonably happily. If that includes a particular sort of support for the kids which you feel is vital to their wellbeing, and which would conflict with you working, then obviously that must be factored in too.
Believe me I know exactly what it's like to look for a job and try to fit in family commitments too ... in my case, when you look at what's actually available within a reasonable distance, what's actually available for someone with my particular skills and experience (unfortunately, in an area which is currently all but dead on its knees), what I can do instead (low paid jobs) and what I'd have to pay on childcare/travel, it's very bleak (i.e. full time hours = practically no take home pay and daughter in childcare which I'd prefer not to do if rewards don't outweigh that). I too have a partner who thinks that because I'm "intelligent", I "should" be able to walk into a high paid job and this has in the past been a huge source of conflict because he just doesn't "get" what it's like right now for 100s of 1000s of "intelligent" people .... let alone when you also have children to consider. I do actually work, in any case, and have done since DD was 2 ... but from home (in 2 jobs !) which often doesn't seem to count for a lot, though the pay is better than I can get right now in a "normal" job. However, I have no pension, no security (well, even less security as am on contract) and absolutely no other perks. It's pretty soul destroying all things considered though DP has shut up for the moment.
It seems here that the way your particular family operates - and what you believe it needs - is at odds with what your DP believes. I'd suggest that that is the issue that you need to thrash out with him - maybe with some counselling if you think he won't listen - so you can both agree a way forward (whether that's together or not). It's horrid to feel undervalued for what you do .... and reading between the lines, am thinking that maybe your DP thinks you're lazy .... or maybe he thinks what you do is "easy" and that you're using it as an excuse not to work (in paid employment - not saying you don't work !). Even if you did describe what you do for your family, it's not up to us to judge you - this is something you and he need to sort out. It's not unknown for men to generally think that women who "don't work" have it easy anyway ... usually because they have no idea what goes on, never do the same things themselves, never have the same responsibility and seem blind to the 1001 things it can take to run a home.
Not saying it's right at all .... but if you do keep finances separate (as it sounds), I wouldn't mind betting that he justifies that because you're "lazy" or "not trying hard enough" (to find a job). Again, all I can do is suggest you talk to him and get to the bottom of what you both think is reasonable, taking into account the extra support you give the kids.