summerflower, you touched on something very interesting here. I really should leave this thread alone now or I will become unemployed, but just wanted to say that this difficulty in articulating the domestic division of labour in non-gendered terms, when historically these tasks have always been gendered, is one of the main concerns of feminism.
It relates to the idea that language is constitutive of power - unutterable is invisible. One of the most prolific philosophers of our time Judith Butler tackles this issues precisely in her book Bodies That Matter: On the Discursive Limits of "Sex". Wiki has a brief description, but it is still full of jargon.
If I may be so bold as to summarise and oversimplify her main idea, it is to do with the way in which one is entered into language and culture differently depending on one's gender - no one functions within a society or uses a language on their terms alone, it is always a social activity that has to be performative (i.e. it materialises through action and repetition). Gender is a constitutive aspect of human existence, which is where the main difficulty stems from - it is impossible to conceive of another human being without taking their gender into consideration, even if their gender identity is troubled in the conventional sense of the word. Therefore, thinking of gender differently is a contradiction in terms, as it actually subverts the very idea which you are trying to analyse and understand. However, this contradiction hides some revolutionary potential - gender is being imagined differently on a daily basis, despite its constitutive constraints. Hence the possibility of set-ups radically different from the patriarchal norm, such as Beta's example.
Or, for a very light-hearted take on essentially the same issue, there is a brilliant song performed by Stan in a cartoon called 'American Dad' (BBC3). Feeling somewhat let down by the divergence of his and his wife's priorities, he signs (DISCLAIMER: this song is a joke borrowed from a cartoon and is potentially offensive):
Stan: She wants to be equal partners? Well, I say no way!
I don't want a partner, I want a wife
Someone who's happy taking care of my life
Where's my Edith Bunker, Laura Petry, Wilma Flintstone?
I want to go back, to a simpler time
When men were men and women had no say
Attend to love, honor and obey
I want to be greeted with a massage and a martini
The way master was by his Genie-e-e-e-e
I don't buy this independence and doing your own thing
I want a woman to make me feel like a king
This ship is sinking and I'm swimming for my li-i-i-i-i-ife
I don't want a partner... damn it!
I want a wi-i-i-i-i-i-i-ife