Would it help to think through the consequences of the various options?
If you stay and nothing changes....
What will happen to your bitterness? Will it lessen, get worse, remain the same?
What effect might that have on your personality and other aspects of your life?
What sort of sex life do you envisage for yourself? Nothing at all, masturbation, infidelity? If the latter, will you do this openly with your wife's agreement, or secretly?
What effect will this relationship have on your son as he grows up and sees very different relationships modelled at his friends' houses?
Will you have any regrets about not having more children?
If you leave and agree a 50-50 residence split........
How will that effect the finances?
Will your work permit that arrangement?
Will you be able to live close by so that your son can travel easily between his homes?
Will your wife want to work on the days she doesn't care for your son?
Will she be able to manage on a reduced income? (50-50 generally involves no spousal maintenance and 50% of the costs of child maintenance)
If you have to work fewer hours, will you be able to manage financially?
You'd be free to meet other people, how does that prospect make you feel?
These seem to be your options, if your wife won't talk about change and won't go to counselling.
You see, on the premise that your wife is not asexual, I'm interested in the pay-off for her in this arrangement. Is her sexuality and happiness in a relationship less important to her than other things? i.e. becoming a mother, not having to work, status, financial security?
The pay-off for you in the status quo is that you get your son cared for while you work, you retain your financial assets, you keep the status of being a married father, you see your son every day while you're at home.
But unsurprisingly, that's not enough for you and it wouldn't be enough for lots of men and women for whom sex and/or love is important.
Of course, none of this deals with your emotional connection to your wife and whether you love her. It sounds like you do, so please don't think I'm belittling that or failing to take it into account. Unfortunately, it doesn't sound as though she loves you as much, because refusing to talk about a partner's unhappiness and the dogged intransigence you describe is in fact selfishness and indicative of a lack of love.
Often these threads discuss the lack of sex and the focus is on that and the unhappiness it creates. Other options are suggested and usually the spectre of getting sex elsewhere crops up.
What tends to feature less in these threads is the acknowledgement that one partner loves and the other doesn't. Or the OP's personal integrity and values as an honest person who won't compromise on them to have secret sex outside of the marriage.
Think through the options - there are undoubtedly more questions than I can think of right now, but in all of this, don't forget what this says about love and care for you as a human being.