But I actually don't want to talk about that issue of plausibility because I think there's a much more fundamental one that makes the whole plot just seem sort of stupid. Namely: why does Magnussen think controlling Mary would help him control Mycroft? (Major SPOILERS for HLV ahead, obviously.)
The starting situation as I understand it is that Mary has a Past with a capital P, one that is not only immoral but dangerous to her and John. Magnussen thinks this sets up a chain of people he can effectively threaten: Mary to John, John to Sherlock, Sherlock to Mycroft. Which gives him what he wants more than anything, the most powerful man in Britain under his sway. The problem is, the chains of influence is going the wrong way, and it's actually hugely improbable to me that this would give him that control. Here's why.
(1) First, there's Mary. Obviously she cares a great deal about keeping her secrets, but a lot of that desire seems to come from wanting to keep John in the dark. She thinks it will drive him from her, that he'd never forgive her. And John hasn't actually done anything questionable regarding her except be fooled by her at this point. So the only way Mary gives Magnussen pull over John is if John decides to stick by her, which seems unlikely enough that Magnussen wouldn't count on it - meaning that the moment he tries to exercise power over John because of Mary's past, he risks throwing away that control.
(2) Second, there's the link from John to Sherlock. Sherlock would do quite literally anything in his power to keep John happy and safe. If John wants to get married, Sherlock will start poking around YouTube learning how to fold napkins into Sydney Opera Houses. If John's safety requires him to throw away his reputation and his friendships and his life in Baker Street and even his continued existence by John's side, then he will do that. Sherlock cares enormously about John's wellbeing, and if John stayed committed to Mary and Sherlock decided this was a commitment that would actually give John a good life, then Mary's past gives Magnussen leverage over Sherlock. But that's a mighty big if. Even if John stays committed to Mary after learning the truth about her (long-shot #1), Sherlock still has to think that John staying in a relationship with Mary is actually going to be a good, safe life for John (long-shot #2). Because it seems very plausible that Sherlock would turn to John on hearing the truth about Mary and say that this is a woman who lied to you at every step of the way, she shot me and would have landed you right back where I did two years ago (my deepest apologies once more for that, by the way, I know that was completely inexcusable), and what we need to do is get you out of this relationship. We need to do it safely, we need to work out a way to protect your child, but Mary is not a woman you can trust.
Put more directly: Sherlock could have decided to protect John and Mary's relationship, which would have given Magnussen leverage over him. But just as plausibly (if not moreso), he could have found a way to protect John by safely extricating him from the relationship with Mary. Some fans will argue that a lot of what we saw post-Lauriston Gardens was play-acting for Mary's benefit, that to keep John and John's child safe he had to make Mary think that reconciliation was a possibility. But even if you think it was genuine, that with absolutely no explanation why, Sherlock was willing to jump from "John Watson is definitely in danger" pulling him back to the dead all the way to "Let me make this dangerous relationship work for John even if it means I have to go to prison or exile so I won't be around to protect him anymore" - even if there's a story we haven't been told yet for why that jump is plausible, that's one heck of an assumption for Magnussen to make, that not only would John want to stand by her side but that Sherlock would decide supporting this relationship was the best way to support John.
(3) And finally there's Mycroft. Mycroft obviously cares deeply for Sherlock in the same way Sherlock does for John, but he's always seemed on the fence about John. He seems to trust John professionally and he keeps an eye on him because John's well-being impacts Sherlock's well-being. But going all the way back to Study in Scarlet, Mycroft wasn't sure that John was good for Sherlock. In TSOT he told Sherlock he shouldn't have gotten involved, we've got the whole "caring is not an advantage" thing. I mean, Mycroft will be there for Sherlock because that's what he does, but I'm not sure that Mycroft's preferred path to making Sherlock happy and hale would be to keep John around, much less keep John around in a relationship with Mary. (I mean, even without knowing what we do about Mary's past, three weeks after the wedding we find Sherlock passed out on a mattress in a drug den and then later that same night mysteriously shot through the chest, so it's not like John's marriage is working out so well for Sherlock.) So again, Mycroft is going to protect Sherlock but Magnussen needs more than that. He needs Mycroft to protect Sherlock by protecting John by protecting Mary.
If I were Mycroft, I'd arrange for Mary to get run over by a bus crossing the street. If I was feeling particularly generous I'd wait until the baby was born. And that's not because I hate Mary or want to see her dead or particularly like the idea of evil!Mycroft - it's that Magnussen makes her a threat to his influence and I think Mycroft could justify the death of one ex-assassin since in his line of business those sacrifices don't seem all that unusual.
And if I were Magnussen, I don't think I'd need Mary. Mycroft has done some seriously shady stuff in the course of the series. There's Bond Air and his brother's involvement. The complete lack of any kind of prosecution for the bombings in The Great Game. The fact that Sherlock was allowed to get hold and try to pass on the Bruce Partington Plans and then his laptop. I mean, all Magnussen needs to know is that Sherlock got his hands on a top-secret government laptop to paint Mycroft as dangerously incompetent (at best) - he doesn't have to accept it, just question how the heck Sherlock even got his hands on it, and Mycroft's career gets nudged into a nose-dive. That's so much more damaging than the whole "your brother is best friends with a man who just married a woman that (a) said best friend met while your brother was completely out of touch for two years, and (b) neither said best friend nor your brother knew about her past or have done anything to cover up."
As I said, it just doesn't make sense to me why a master blackmailer would take Door #1 in this scenario. If his real goal is to control Mycroft rather than just make life miserable for Mary, this plan seems pretty far-fetched and not at all the most likely course to get him that control.