For the stuttering more around you and your wife and yourself, that’s how it is for me with my parents. Not sure why, but I’ll stutter 10 times worse around my parents than random people. Maybe it’s because I’m relaxed around them, but why do some people stutter more when relaxed than they do not relaxed? As for what you can do for him… It’s really hard to say, because everyone has there tips and tricks that work for them. For me as kid using my hand to tap on my leg worked a little bit. You can also try giving him a little squeeze ball. Sometimes distracting can help with stutter. Long term help though, I’d look into a stutterer help ‘camp’. I’d wait until he’s a little older though. I went to one when I was 12ish and I was to young to put anything into practice or practice on my own time. The one I went to, I’ll post the link, was really good. I saw grown men who had dealt with this their whole lives leave being able to speak 99.9% better. Of course I’d advise doing your own research on it and see what best suits you. Hope all goes well for you and your kid. https://www.fluentspeech.com/about/