Welcome to the forums, and thank you for sharing your story. I'm really sorry to hear that you're struggling with your relationship at the moment. It must've been quite an emotional rollercoaster ride for you when you found out what your husband was doing, and your feeling of frustration of trying to understand what and why did he do that is completely valid.
While I'm not a professional relationship counsellor or anywhere close to that, I hope you wouldn't mind listening to my perspective on this matter. I feel a relationship is formed when both couples do their best to meet each other's needs. It's a never ending journey of team work and support between the couples, and they'll do their best to work through conflicts and come to a mutual agreement. But when one partner feels that their needs aren't met by the other partner, they would seek that fulfilment elsewhere. It is possible for emotional and sexual needs to be separated, even though they both are generally bundled up together (some people take sex as a way of spiritually bonding with the person whom they're in love with on an emotional level. Some may just take it as a way to fulfill their sexual desires).
With that said, you mentioned that you have two kids and recently that you've been very occupied by them. I can understand having kids can be very handful, especially when you have more than one. The role of a mother is a very hard role, and I admire your ability to fulfill that role for your kids. A mother's priorities would change depending on the kids and family, and it gets really hard for a mother to balance between the role of a lover to their husband, and a mother who cares for their kids and family.
It's very noble of your husband to be going to extreme lengths to show how committed he is to you. He may be feeling a heavy sense of guilt for doing such a thing, but also confused on what he wants, and needs some time to discover that. Perhaps, take some time to talk to him about it, listen and validate his needs while communicating yours as well. I feel your reasons for neglecting him when he tried reaching out to you, is a valid reason (maybe too busy with kids or house chores, and just too tired at the end of the night?).
Hopefully that perspective may help you understand your husband a bit more. Happy to chat more to you as well Syliva0071.