Significant other not in the delivery room?

Has anyone ever chosen NOT to have their husband in the delivery room? Here’s the situation:

I’m scheduled to be induced at midnight on the 28th. We already have an 18 month old daughter, and we haven’t been able to find someone to stay with her that night or the following day. Our babysitter fell through, and we have no other options. When discussing what our options were, my husband suggested that he stay with our daughter the entire time to allow my mother to be there with me. He’s not crazy about the birthing process as it is, and he knows he’s just not the best supporter. With our daughter, he basically just stood in the corner of the room and let my mom comfort and coach me through the process. So, I guess my question is, would it be awful to do it this way? I know it’s extremely unconventional, but I’m not sure what else to do. I’m afraid that if I choose to have him there, but not my mother, I’ll end up having no support. I’d obviously never ask him to miss the birth of his child, but he offered and genuinely seems kind of excited to have the option not to be there. (I promise, he’s not an awful person, just really awful with gross, medical things.) 😂