If you want your kids to stay asleep, forget the Blues Jr.
True, it has a master volume. But I've found that the range between 0 and 1.5 goes from "I can't hear it" to "Wow! It's pretty darned loud!" And the knob twists all the way to 12! Just barely tapping it with your finger makes a huge difference in volume when you're below 2 (and 2 is too loud for the kids' bedtime, I reckon). This is my only complaint about the Blues Jr.: Great sound, but the master volume is too sensitive, and basically useless at lower volumes.
I agree with other posters that, if by "tube tone" you mean "distortion," you're out of luck, even with an attenuator. But, if you're really just looking for warm blues tone that sounds nice, full, and juicy, you've got options.
For an off-the-shelf, affordable solution, I'd recommend trying a Champion 600 with a decent pedal in front of it. Maybe a Boss Blues Driver, a Digitech Bad Monkey, or something similar. I've also heard good things about the Roland MicroCube. Good tube simulation and it sounds passable at low volume levels. Also comes with its own effects... kind of a nice bonus.
Others will have their own excellent opinions, and I'm sure someone will be able to point out an exotic, custom, or modded solution, if you have the budget, the time, and the know-how.
You could always try earplugs. For the kids.
Whatever you decide, let us know what you end up with and how it sounds!