I am hardly an expert, but a few thoughts. First, it looks like there may be some rot in that wood — is that rot on the edge that we see? And there may be rot in the crack itself. I would assume any rot would weaken a repair made with PVA or cyanoacrylate. There may be be extra gaps in the crack. Keep in mind that PVA is not very good for filling gaps and any glue that is in a gap will not have much strength. And even if the glue itself holds, it might be tied to wood that is itself still weak if there is rot. There are products called penetrating sealers made with epoxy. They are often made initially for marine purposes. They penetrate and strengthen rotting wood. I have used Smith’s with some good results. I do not know, but Smith’s may also make marine quality epoxy glues to fix the crack itself.