Does an AI have Free Will? A difficult question even in our reality.
I think Bob is a sort of magical AI, and he has Will. But it isn't Free.
So what is Free? That's not clear either here or in the Dresden Files, but in terms of the latter I would say it comes down to the ability to change yourself, your very nature, which by definition (of the Dresden verse) changes reality. We know that Choice spawns universes (in an Amber-style broad-spectrum). Bob cannot do this, and nor can most supernatural beings.
But that doesn't mean that Bob is mindless. It just means he can't stop being what he is. Only a Free Will, a mortal Will, can change him. Which is precisely why he takes on the personality of and is loyal to the owner - with some clear exceptions. It's obviously complex, and Harry's naming of Bob I think helped shape him more than any other since Kemmler.
So Bob can make decisions in line with his nature, his "core programming" if you like, but cannot act outside those parameters.
Edit:
With regard to the original question posed by the OP. I do think it's possible that Harry could have a third child eventually, and l wondered similarly to you if Elaine might be the mother. I feel like the next child will be male, and similar to Mordred of Arthurian legend, he will eventually try and kill Harry (and perhaps succeed - although as we know there are levels to the whole death thing).
I now more subscribe to the theory that several others have mentioned in that it will be his child with Lara. A resentful, angry being like Thomas. Bred to kill him by Lara, and to rule both the White Court and be a power in the Winter Court (like the Erlking or Vadderung). It fits a lot of tropes, and it would be a good move for Lara long term. A means to control Harry and eventually defeat him if necessary. I suspect this child could well be stronger than Harry too. And the Child's downfall will be Maggie, of course. Or alternatively, Jim will have him join Team Dresden at the end and all will be well. Depends on how dark Jim goes.