To be honest, I think how your financial arrangements are currently is probably having an effect on your general self-esteem regarding what you are contributing to the pot. I would hate to ask for money for things like hairdressers too.
It is doable though - here's how the finances work in our house.
Pre-kids when we both worked FT, we had our own accounts, and a joint account for household bills and other shared expenses such as car servicing etc which we both paid set amounts into. He paid more as he earned more. He also paid ALL mortgage (he did earn a LOT more than me LOL!)
Post-kids and as a SAHM, I stopped paying into joint bills account. (He upped the amount he paid in to cover it.) I got all the CTC and child benefit paid into my account. He ALSO then added me as a joint account holder to his own personal account so that I could use "his" card for supermarket shop, and most things the kids need.
We agreed that for things like mine and kids hairdressers appointments, makeup and for my clothes (essential clothes that is, not frivolous spending on stuff I didn't need), daily spends (bus money, pressies, mums and tots groups etc) then that would come out of my own account (CTC & child benefit money) so that I wouldnt' feel like I had to ask him for that type of thing. (I don't see the CTC/child benefit money as being specifically for kids - it just adds to the whole household pot really).
Anything the kids need generally comes out of our joint current account as it's usually clothes from supermarkets that I buy from time to time while doing a weekly food shop (again - that now comes out of what had been solely his own account).
A year after DS2 was born, I went back to work (just on a Sunday - DH minds the kids so no childcare issues) and I generally also keep that money for myself (couldn't afford to socialise or buy much for myself on just the CTC/child benefit total). That bit of extra money that I've actually gone to work to earn has really helped my self-esteem and also means that when our joint current account is going overdraft mad, I can top it up with the money I've earned. I have also been able to pay for ALL the kids' Xmas pressies out of my account too.
As regards DH's own personal spending, we both agreed that of course, he should spend as he needs to with regards to his own clothes, shoes, socialising etc. We both know what is going on in all accounts at any one time, and like I say, if the joint current account needs topping up, then that takes priority over what's in my "pin money" account and I transfer some over.
I think the whole thing just needs a big discussion between the two of you. No matter who earns what, it IS possible to sort something out which works for both of you, as long as you both have similar outlooks and agree not to spend on daft, frivolous stuff (guaranteed to get the other's back up and end in an argument!)
I know that was probably very boring, but household finances ARE boring. No-one likes to have to think about them, but it causes no end of bother in relationships if one harbours resentment, and like I say I think it might possibly (along with your pg hormones!) be part of the reason you are feeling a bit unnerved by this woman (who is still earning, still socialising with your DH, not looking harrassed or feeling dowdy as most of us do after having kids.)