I agree with "flyfromdenver." The safest route is 3 seats together. While I don't doubt that UA will do their best to get you a bassinet assignment, it is still based on best efforts and other passengers they need to accommodate who may have needs that end up trumping yours. There are other things I've seen happen: the bassinet might not be loaded, is broken, isn't up to your standards, etc, etc.

I'd never book seats "hoping" anything. In my years of traveling with a kid, the best thing I ever did was buy the extra seat. Many, many flights to Europe my kid just slept on a blanket on the floor or in the car seat. If you put everyone on the same ticket, you're pretty much assured that you'll have seats together (understanding, yes, that sometimes even that gets screwed up). That gives you much more flexibility than a bassinet.