Hi OP. I've read your responses but not RTFT, so apoogies if someone has already pointed this out, for the essay that follows and if I'm completely off the mark.
It sounds like the problem is with the work balance here and the sex is a manifestation of that deeper problem. You appear to be a bit resentful of the fact that your DW was not willing to increase her hours at work and let you look after your child more (i.e so that you both have a more equal share of childcare/work) and in response perhaps? you are not doing as much at home as you should (or your DW thinks you should). You said yourself that this was a sore spot; you wanted your DW's position and your wife thinks you don't do enough around at home. So I think your answer is there.
If it is, I don't think the sex situation is going to get any better until this is sorted out. On the one hand some of your responses are a bit ridiculous 
: your posts seem to suggest that by working you are doing more to care for the child/ under more stress/work harder that your wife. However I am a big supporter of men being involved in childcare, so your wife refusing to have a more equal arrangement did make me see things differently and I have sympathy for you on that front OP.
In her defense:
a) you said you had a conversation about work/childcare towards the end of her maternity leave? Was the current situation the first arrangement and you wanted to change it? If so I can see her POV as the current arrangement may have influenced her decision to have the baby. However at the same time you're not entirely happy, so again, sympathies to you OP.
b) you did agree to the arrangement and you can't continue to resent (or punish) her. IMHumbleO, the default should be that each parent spends the same amount of hours working, whether that be at your NHS job or with the child, and you should both have the same amount of free time when not working (at a job or with the child). This should obviously be amended if one of the parents is clearly struggling.
I would start with a serious reevaluation of the hours you are spending working and the hours of free time you both get. If you are working less hours than your wife I would sort that ASAP.
If you really are working the same hours and have the same free time, I would argue against your first response to say that you should be prepared to put in a few extra hours to take some pressure off of your wife. At the end of the day, you still feel able to have sex (i.e you are functioning as you were before and seem to be coping well from your posts) and she does not (i.e she is not coping as well as you are). It doesn't need to be indefinite, obviously. If that makes you feel resentful (and your posts really do indicate this, not necessarily resentful due to lack of sex, but the working issue) then you either have a lack of empathy for your wife and/or an unrealistic view of the strains of childcare or (and this is what it seems to me) you're resentful because you offered and wanted to split childcare and work-time more equally between you both and she declined. Now you don't feel it is fair to work and to spend more time doing household things.
If it's either of the first two (which honestly do not come across in your posts but I don't know you so am throwing it out there anyway) you probably deserve the flaming you're getting, and I'm not sure anyone can make you think differently but perhaps counseling can help. If it is the last, then the childcare arrangement is clearly a sticking point and needs to be addressed asap. Counselling might also help here (have never done couple counselling so can't recommend, just something you might want to think about). Is it too late to change the childcare arrangements? If it isn't, talk about it and try to come to a solution where both of you are happy and not resentful. If it is too late, talk about it anyway, as you both still need to get over this and feel supported and non resentful. Hopefully then you are both happier and any other issues that stem from this (i.e. sex) will also resolve themselves.
Good luck OP!