Thanks for sharing your story, Rick. My wife and I lost our first pregnancy due to Turner's Syndrome, so I'm painfully familiar with how random the genetic lottery can be. I'm happy to say we have a healthy, happy 17-month-old girl now. I'm glad to hear Noah is doing well, and I'm heartened to hear how proactive the doctors are being.
First off, I'd just like to say that you're doing a lot right. You have a well-designed site with great content, a good core structure, and many of the important features of a modern site/blog. The wide world of SEO can be overwhelming, but it's rare that you need to tackle it all at once.
I think it's great to be thinking proactively about categorizing your content, and it's ok to let that evolve organically as your needs are clear. Categorizing the videos certainly makes sense.
At this point, though, given that your basic structure is good and you've got a lot of content, the social and link-building aspects are probably equally or more important. You have one tremendous tool at your disposal - sincere passion that can connect you to an audience. Your own outreach efforts, interactions with other parents, discussion boards, communities, etc. will go a LONG way. As you build relationships, links will start building themselves.
One thing that wasn't clear to me until I fully read your post and dug into the site was that your wife is a pediatrician. The "Mom MD" just read like a cute category name to me (no offense intended - that was just my first impression). This fact, IMO, adds a lot of credibility to what you're doing, and makes this more than a personal blog. I'd make this clear, especially on the About page and at the top of the Mom MD section.