There is a bit of a double standard view of this on MN, in so much as that if it's a woman who doesn't want to have sex then the man needs to be understanding of the fact that she is looking after the DC/has had a baby within the past ten years/shouldn't be expected to have sex with him and does he contribute towards the housework. Whereas if the man doesn't want to have sex the woman can (rightly) feel hurt, the question is asked as to whether the man is getting it elsewhere i.e. Porn/OW, an anyone who dared question whether the woman contribute more in any way would be flamed to hell and back.
Sex is a very divisive issue within any relationship, and tbh there's no right or wrong answer. Nobody, be that man or woman, should feel that they have to have sex with anyone they don't want to. But when this happens within the confines of a supposedly loving relationship it's not wrong for the party who wants sex to question why this won't or can't happen. And I do think that the less you have sex, the less you would want it, so it becomes a bit of a vicious circle.
If you cut back to basics it does come down to love, and the rest can be built on from there. Do you love him OP? Does he love you? If the answer to those questions is yes, then you both need to open the lines of communication, and understanding, and go from there to bring your relationship back on track. It seems that at the moment you have both been stuck in a rut. You want him to contribute more and you feel bad about yourself because of your depression, whereas he feels that since you have had DC everything has changed and he has fallen to the bottom of the pecking order.
You need to be able to meet in the middle on this. He needs to realise that coming home and throwing everything where he lands isn't going to endear you to him, but equally, if he's working a twelve hour a day manual job it's understandable that he wants to come home and sit down and relax. Being a SAHM is not* more difficult than having a full time job. It's different, and there are equal demands, but it's not the same.
Also, with regard to any illness, there needs to be understanding of all the parties involved. Living with someone with severe depression can be very difficult, and there often seems to be a view that the person with the illness (any illness) is the only one whose position is important, whereas the people surrounding that person and also living with the illness need to be there for that person only and be understanding of that person's needs while completely distancing from their own.
Can you sit down and have a conversation at a time when neither of you has become frustrated about something, and talk about how you can bring the relationship back on track? A conversation which doesn't resort to him talking about his needs and you talking about your needs and where you're both talking at each other rather than to each other.
So the conversation would need to go along the lines of that you both have differing demands and viewpoints and it seems that these are causing friction within the relationship, so how can you make some middle ground? I.e. Take at least one night a week to both just put down everything at the end of the twelve hour day and spend that time together, having dinner/having a conversation/going to bed at the same time, even if that isn't going to lead to sex yet. Assuming the two year old sleeps through, the washing up will wait a couple of hours and nothing is that manic with a two year old that nobody gets a single second to sit down, you can sacrifice one evening to spending it with your DH.
However on the other nights not throwing clothes on the floor/gaming all night but both winding up the day together, making/having dinner together, clearing up the kitchen together thus enabling time for conversation, and when the kitchen is cleared both settling down for the rest of the evening. Reconnecting with each other is the first part of getting your lives back on track as a couple. But you both need to be open to having some input.
But as I said above, it all needs to come down to whether you actually still love each other.