(Working in a call center was actually one of my last jobs before going back to lots of school for a big career change. And scheduling control will actually be one of the benefits of the change.)
It's a hard question to answer because, if you're starting a new path, there are so many job paths to attempt. There are certainly other jobs besides firefighting that may have better schedules than the one you have, so you have to ask yourself "why firefighting?"
For example, I have an acquaintance who was finishing medical school and chose to do emergency medicine because of the schedule. They can work ridiculous shifts but then have loads of time off, depending on how you and the hospital want to set it up. (We're talking every other week off.) He was right about the schedule, but he underestimated how much the job would drain his soul. Now he apparently regrets choosing it, wishing he had just done family medicine.
My point is, if scheduling is what you're going for, and if you're willing to do some extra training such as firefighter school, I have to think that there are many options besides firefighting open to you. Firefighting might be the right choice. But I don't think scheduling is the single reason that should guide you towards it, especially if you're hesitant about the other aspects of the job.
Reading between the lines, though, maybe there are other reasons firefighting interests you right now? You have some proximity to it right now as a dispatcher, it probably wouldn't require too many years of your life to switch into it, you probably wouldn't have to move cities, it's a very respectable vocation, it doesn't have a lot of employment uncertainty (as far as I know)... many of those things may feel emotionally desirable to you right now as a father/boyfriend.
So, it might be the right choice for some of those reasons, but make sure it's for the right long term reasons.
My general feeling is that, if you are willing to put in the resources to switch careers and you're young enough to make the investment worth it, make it a damn good switch.