Him checking into a hospital sounds like a really smart move. And I'm really keen on the idea of ptsd sufferers having someone love them and support them warts and all, so I hope it works out for the 2 of you. I really do.
Him running is common, ptsders do that. Every 3 months though, sounds like he's really struggling (so again, yay hospital!). But maybe ease up just a fraction. Engaged? No need to kneejerk and call it off, but maybe let him know that there's no rush.
Doing the maths on this, you probly know it doesn't sound great. Bub #1 is 15 months old and he's getting mama #2 pregnant. And if the twins are 1.5 y-o, and you've been with him 2 years...
Like I said, sounds like he's really struggling. Like, a lot. If he's proposed to marry you, but can only handle life in 3 month intervals? If he walks out on relationships with kids? The reality is he's really unstable.
With treatment, his behaviour could totally stabilise. Just know that you're in for a bumpy ride, big committments seem to make him panic and flee, and that though he will potentially (no guarantees unfortunately) stabilise with proper treatment, that means he's also going to change. In a lot of ways.
That's not to say he's going to change into someone completely different that you couldn't possibly love. But right now, the reality is this guy is really rocky, and has been racking up commitments that he can't stick with for several years.
Please, don't take this as "You gotta let this go". It's not that at all. Just a bit of a reality check. The fact that ptsders often cope by running, doesn't make it any less of a bit deal. He's reaching overload with his current life, he's reaching breaking point, every 3 months. Not a great scenario:(
But, fingers crossed for you that his hospitalisation is the first step towards some positive, life-changing stabilisation and good health for both of you.