I'mma say this to you because I literally got clarity on it from my mother a few hours ago.
Don't try to "stay strong". Cry it out my dude. If you're not comfortable doing it in front of your wife or other family, go into a room by yourself, your car, wherever... Do that shit and let it all out. My suggestion is to do it with your wife at a minimum, because she's going through the shit and likely needs that from you.
I got some shit on me that I've been going through very recently. Some shit from my past reared it's head and has pretty much fucked up my life. One of my wife's biggest issues with how I'm handling it right now is that I'm showing next to no emotion other than anger and occasionally laughter if I see something on TV that brings it out. My problem is that I've held my emotions in check for so long that I almost don't know how to feel anything any more. My mother and I had an email exchange earlier today where I vented to her and I mentioned that guarding my emotions has caused a number of problems, but I keep doing it because any time I've ever let my guard down someone uses it against me. But keeping it up caused a huge problem between my ex and I. After 23 years, my mother finally found out today that my ex and I were expecting a child at the beginning of '96, only to lose the baby early in the morning one day in Feb. My ex was hemorrhaging so badly when it happened that I scooped her up, put her in the car, and drove her to the hospital as fast as I could. After a while the doc came out to see me and told me there was nothing they could do to save the baby and also told me that had we waited for an ambulance she likely would have died due to the heavy blood loss. They did a D&C and after a series of blood transfusions we went home a day or so later. My ex was really fucked up over this. We lost a child, she nearly lost her life, she couldn't work for a while, and she was an emotional wreck. She was only 20 and I was 23 at the time and I wasn't prepared to deal with anything like this at all and felt I had to "stay strong" for her, which I did. I showed next to no emotions and kept pushing forward. I never really talked about it, and I kept a wall up in order to keep it together for her sake. Doing that led to possibly the worst argument of our relationship, where she was mad because she felt I didn't care about what had happened, and when I tried to explain to her that I was simply trying to be strong for her it all hit me at once and I finally broke down and cried. The damage had been done to our relationship and a few months later we broke up.
I wrote all of that to say this: Be there for your wife, but don't ignore your own emotions. Don't bottle that shit up in an effort to "be strong" for her. You just lost a child, no one would ever hold it against you if you allowed yourself to grieve. If you gotta hold her in your arms and cry together, do it. If you gotta do it solo, do it, but whatever you do, don't hold it in. If there ever was a time for a man to allow himself to feel his most vulnerable, it's after the loss of a child.