I don't read into it that she doesn't put any priority on her relationship or that she doesn't like sex or that her relationship is over or that she sees sex as giving herself over to a man 
It read to me that she is saying a real partnership involves not 'giving yourself over to a man' it's about sex being mutually enjoyable and about respecting yourself enough to not just give in for an easy life and instead expect a male partner to respect you enough to not pester for sex.
The way around it for a man is to take over more of the parenting so their partner is not getting touched out and feeling overwhelmed and burnt out by kids.
It's not fair to expect a sexual relationship to stay the same through childbearing IMO. Or to keep pestering an unwilling partner for sex.
Being burnt/touched out doesn't last forever and her male partner had an equal amount to do with them having 4 kids TBF.