How to respond to threats by disgruntled, powerful former collaborator

Right now, given the lack of details (and maybe you don't want to add more), it's hard to say what to do. One thing that would be good to know is: what are you actually worried about? If you are tenured (I guess mid-career means this), you don't need to worry about that. What sort of influence does this person actually have? Disputes happen from time to time, and if your collaborator is a jerk and people know this, they may not pay much attention to their rantings.

That said, my suggestion is to reply with something along the lines of:

Sorry we neglected to mention my preprint with you. That project came about independently, and I should have told you about it earlier. I've added an acknowledgement and a reference to that preprint. See attached. Other comments welcome. By the way, what do you want to do with our preprint?

From my point of view, it makes sense to mention your preprint from 3 years ago in your newer paper, and being generous with acknowledgements costs you nothing. (Presumably you've had discussion about related things, which, even if your colleague did not actively contribute to your understanding of things, may have been helpful in some ways. Though again, I don't know the specifics, so you have to decide this.)

Even if you can win, no one wants to get into some big fight about who had what idea when, so if there's a reasonable way to mollify your colleague, it's probably worth it. Admittedly, your colleague doesn't sound reasonable, but if you add an acknowledgement and reference to that preprint, I imagine most people would think you behaved ethically even if your colleague goes on a rant-page.

You should also discuss this with your present coauthors before doing anything.

Before you do anything else, first of all, secure your full independence from the prior professor. It includes funding, reference letter, community work, committees, etc. Don't answer any of his e-mails in this period; answer only some else's questions regarding your relationship.

Second, save the proof material: the old copies of what you did with him, e-mails, etc.

Third, only then reply to the old guy. Insist on your viewpoint and threaten him back, telling him that in case of claims from his part you'd issue the counter-claims from your part. Remind him that false accusations can be legally prosecuted. If he did issue false claims, actually check whether you are right from the legal viewpoint and perhaps proceed with the help of the attorney.

Fourth, proceed with publication as you wished.