Congratulations! You might not be riding single track for a while, but yes it won't be long before you can attach a trailer to a bike and ride with your little one. And I would think the mountain bike would be better suited for that than a road bike.

Years ago I used to do long road rides with a certain friend. He decided a month before the birth of his first child that he would do one century per month for the entire year (to which I laughed and said, does your wife know?). Anyway, that plan quickly evaporated. But before long he was hooking a trailer up to one of his bikes and riding with his son on local trails to various county parks. A couple of years later their daughter was born and soon she was joining Dad and Brother in the trailer. The kids are in elementary school now, riding their own bikes or with Mom or Dad on a tandem. Over the years they have visited every park and playground in our county (and there are lots of them), always traveling by bike.

Maybe someday my friend will do long rides with me again, but for now he is enjoying himself quite a bit with the riding that he's doing.

Good luck with your next chapter!