Which is less professional?

Showing up with the child would have been disastrous.

I hope she called and explained the situation and gave them a heads-up that she would be a little late? That's the only acceptable way to deal with this kind of thing. If she just showed up late, she's probably not still being considered for the job.

I'd say both scenarios are equally unprofessional. Showing up late for an interview is one thing and bringing a baby is another. That shows the employer that you have poor time management and planning skills. First impressions are important. It's a safe bet that your wife is no longer considered for the position.

I'm 100% with rtfm on this. Calling to let them know she was running late would be the most professional. I would never take one of my kids with me for a job interview unless I was intentionally trying to tank the interview. Showing up late without bothering to call is unprofessional and in this market that's more than enough to cost her the job.

Showing up with the child would have immediately stopped her from getting the job, no employer needs that hassle.

I would have called and let them know about the lateness, they would appreciate the proactiveness and honesty. She may not have gotten the job for being late, but she definitely wouldn't have gotten the job if she showed up with an 18 month old child.