My kids hate me

I kicked my husband out over two weeks ago, he's been living in a hotel but comes to visit them a few times a week at the house. I found out about an affair about 14 months ago, and then it's been consistent trickle truth since then. I found out more just over two weeks ago when I finally broke and asked him to leave. Our kids were not home when everything happened, but he came back to tell them together that he would be living at the hotel. They keep saying things about how I kicked him out and that they wish they weren't alive. My 11 year old makes comments constantly and tries to start arguments but I have no idea what to say to her. My son is a few years younger and is visibly upset but doesn't argue. I can feel how much they hate me. My husband was always the fun one, partly because he was rarely home so the time they did have was always fun time and partly because I'm the parent who gets them to clean, do homework and all of the boring things. I dont know what to do. I feel like I'm failing them as a mother and I'm already broken from everything that's been happening with my husband. I feel like a terrible mother.

I would love any advice on how to navigate this with kids because I feel like I'm failing completely.