I have nothing more to add to what DnJ said. I co-sign 100%.
I want you to know that I feel your pain because I've also gone through it. I didn't show any of my true emotions to the kids and just took time when I could to let it out in private.
You gotta just get into 'Dad' mode and not 'You' mode. The You will have time to process and recuperate. I know it sounds easy to say but I know it's not easy to execute - it $uck$ big effin' time, but you do it because you're the Dad. It's part of our job description.
One of the things that I keep in mind with my kids is that whenever they want to do something with me or show me or whatever it is that they want my attention, it is a 'bid for connection'. Esther Perel talks about it. And so, I just remind myself that my kids are just trying to connect with me and be closer to me to show me whatever it is they're super into right now. And I get super into it for them, even if it hurts in the moment.