J., I completely understand where you are coming from. Don't beat yourself up over it. I think it's a normal reaction to your situation. I had a premature baby almost 2 years ago, and our oldest son was 5½ yrs. old at the time. Our preemie only had to spend 16 days in the NICU, but once we got home, life was turned upside down. While in the NICU, my husband and our family's had moved us into our first house, so life was chaotic, living out of boxes, trying to get our oldest back and forth to preschool in another city, 20 minutes away, after having no sleep the night before from being up with the preemie all night while he nursed and had severe bouts of acid reflux.
Our oldest missed quite a few days, the last couple of months of his preschool days, and I completely regret it, but there was not much I could do about the situation.
I was completely exhausted and many days I would tell him to make his own bowl of cereal or sandwich. I taught him how to do these things, so that it could free me up a little bit. Some people told me I was being unreasonable for a 5 yr. old to make his own sandwich. I don't think I was, given the circumstances. My preemie nursed every 2 hours, for almost an hour each and every time, for months on end. I felt guilty because I didn't play with my oldest as often, or read books to him as much as I had done previously. But you know what, it ended up being a temporary thing and eventually, we got back into our normal routines, and he's fine. We did ask family to kinda help pick up our slack by taking him for weekends and for play times, etc. so that he COULD get some one-on-time with other family members, at least. So if your kids have grandparents, aunts/uncles close by, I'd ask them to pitch in and take the older ones for a little while. Even if just to McDonald's play land for a couple of hours one afternoon. Also help include them in the care for the baby. Ask them for help during changings and feedings (I don't know if you're nursing).
And I'd also speak to your doctor about these feelings. You may need to be treated for PPD a little while, just to get you over the hump. I wish you much luck! Just hang in there!