I can't speak for OK, that's why I asked for her county so I can research, however, here, it is completely up to the parents who visits the child while in juvenile detention. Doesn't matter that jr. is family, however, some counselors in the detention center may (barring there aren't any dv issues or other criminal issues) allow mom to bring jr. to the center (if she herself is an adult) to facilitate the visit.
She didn't mention it and it looks like she may have wanted to if you read the sentence, but it looks as if he wanted to say he just turned 18, which makes me wonder what her age is. If she is a minor, I don't see her being allowed to visit because then the detention center would now have to involve HER parents as she is not allowed to visit on her own. Sure, his parent's would be allowed to bring baby, but her, I'm quite sure not, especially if his parent's are already against it.
Now whether or not I'd allow my child to visit is a completely different story. 19 months or 19 years old, I don't want my kids anywhere NEAR a detention center, jail, etc. My oldest is now a deputy sheriff working in the jails, that is the only reason he's allowed in one now...
however, there are many programs that take kids back and forth to facilitate a relationship with the parents and I can see both the bad and good in programs like that. It's just not for my kids, however, even with my ex, I don't see him going to jail (unless of course it's for non payment of support...LOL)