Jealousy is a signal. It lets you know you're not fine with something. Then you need to know what that thing is, and whether your signal means "stop everything" or something different.
She is entitled to feel jealous, yes. It's important that she isn't made to be ashamed of her feelings. And yes, they are natural. But then you need to identify what the problem is.
Because monogamy is portrayed as the "normal" and "right" thing, I assume everyone she asked would have told her that she can't let you do that, that it's wrong, etc.
But this image of someone who matches you 100% and fills 100% of your needs 100% of the time is wrong and flawed, and that leads people to be disappointed when it doesn't happen. So one thing is definitely to get used to the fact that no, this is not a realistic scenario.
Mind you, monogamy is possible, and works for some people, and nothing else would work for some people. But that doesn't mean it's right for everyone.
A lot of the jealousy comes from "am I not enough?" and "will he leave me?" kinds of questions. In this cases, reassurance is important. The jealousy doesn't come from your actions as much as it comes from her insecurities. A jealous person will be jealous when they have no reason to be. In this case, society leads her to believe she has reasons to be jealous. Your role is to show to her that she does not, or in other words that you won't leave her for J, that you won't love her any less, and so on. It might be slow and it will be hard, but it is possible.
It is definitely a good idea not to go further until she is comfortable. And that might take a while and be frustrating, but otherwise it will be worse afterwards. You can't ignore problems, you need to work them through.
I agree that the child comparison is weird. The first thing that comes to mind is "I don't have sex with kids". I used it for the feelings though, as many people don't have trouble believing you can desire more than one person, what remains is the feelings, and they're not dependent on sex. I also use comparisons with friends, too.
But also, there is the fact that from the post, I don't think there is a sexual relationship between J and the OP, so focusing on feelings is a good way to go, and as the mother of several children, I felt she would be able to understand that love doesn't divide, it multiplies.