Leave him to look after his baby by all means, but let him know, even if it's after the school run.
One day, a few years ago, my wife didn't come home from work. She's usually in after lunchtime. I assumed that she was out shopping, seeing a mate or whatever. I picked our girl up from school and took her to the park, then we went home and I made dinner.
Her and her sister have a business and on Fridays, she does 5am to 11/12, comes home, sleeps and goes out for a night shift at midnight.
After 6pm, I started to phone her, with no reply. I thought that she must be having a late one, or driving. By 9pm, I rang the Police, asking if there had been an accident, involving our car, on her likely routes home; they called back later, saying it hadn't been picked up on ANPR. I kept ringing and eventually, she answered in a rage, as I'd woken her up.
She'd decided to sleep at her sister's and thought that I would have known, despite her not having done so before! She also said that she'd heard the phone calls, seen it was me and not answered, because it was annoying! She really didn't think I had any right or reason to be worried.
And no, there was no row beforehand.