I think it's also important to realize that, because this has been a poly-fi relationship, this is all she has. Of course she's hanging around all the time, of course she doesn't know when to leave, when for all intents and purposes this IS her family, she hadn't had the option to build another one. After the break-up, maybe she can think about finding a primary partner of her own, someone whose bed she's actually allowed to sleep in, and building a home where she's more than a (often unwelcome) guest.
Matt, your feelings are not inherently wrong. There's nothing wrong with wanting to break up with someone or wanting space. You did the right thing by being honest with your wife, and I commend you for planning to break up with Si in person.
Maybe it will be a smooth adjustment to a less time-intensive vee, or maybe there'll be a big fight, and then again maybe this really is untenable, maybe in the end Si won't stay in your wife's life, as would clearly be your preference. It's just awfully sad to watch (albeit secondhand and from a distance) someone who's devoted her time, energy, and fidelity to the two of you and your children be met with resentment (I certainly wouldn't say that you come off like you hate her, but you've been very clear that you resent her presence) in return.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.