First of all, I don't think you can have a healthy relationship without sex, unless both parties have low sex drives and have an agreement that hardly having sex works for them.
So this isn't something that you can just accept and tell your husband to deal with. There are other posts of women in the reverse situation, and having told them it's not fair that their partner ignores their sexual needs completely, I am not about to turn around and say differently to you.
So you can't just ignore this. However, that does not mean forcing yourself to have sex when you don't want to. That's something no-one should ever do, even the thought of it is awful.
However, you do need to work out why you are feeling this way and figure out a way forwards. And most of all you need to talk to your partner about it.
You need to figure out what's on your mind and get it straight in your head before discussing it, and recognise that he might need some time to get his own thoughts in line, so it will probably take a few conversations.
From the sounds of it you need to address:
Whilst you appreciate that he does help with the children, you still feel like you are doing more than the lion's share, and it is leaving you exhausted. Is there any way that you two can figure out how to better manage the children when you are both there?
That you appreciate he is probably stressed as well, but it seems like your stress is affecting your libido. This is very common. It's important that you recognise that he is probably stressed with work as well though. Stress just affects people differently. What can you both do to help each other?
Your confidence is very low at the moment, and you need some time to work on that. This is something that you do actually need to do proactively. I'll do a separate reply on this. Your partner can help with this, but it's really you who determine your level of confidence to a degree.
You did enjoy sex with him beforehand, and he is a good lover. You really loved the fact that he wasn't a selfish lover in bed, and you would like to get back to being more sexually active. He will appreciate you saying this, because he is probably thinking that you think he is terrible in bed, and now the children are born you have no need to "tolerate" it!
Finally, you could suggest going to couple's counselling (something like relate?). Not because the marriage is in such a bad place that you need professional help, but because it might help to guide your discussions on these issues, and they might have some ideas that you guys won't think of.
Finally you both need to commit to taking this forward. You guys are a team - you can work on this together.
It's worrying that you think of sex as a chore - sex should be a wonderful thing which brings a couple closer together and continues to solidify their bond. You don't need to wait until you collapse in bed - try and work out different times that you guys could do something. Even if it's not sex straight away, maybe you could get the kids to your parents for an afternoon, have a date night, and kiss for a while.