Recording Environments

Nothing wrong with a little natural ambience.  You could always shut the girls in the kitchen with a tub of ice cream...

I'm also in a similar "acoustical" boat.....I've got a 3, (soon to be )5, & (soon to be) 7 yr. olds that get all excited when I fire up the DAW, but all they want to do is just bang on the keybord......(while I change presets for them).......so, most serious recordings have to be done after they go to bed.
 
They do like to sing, so I'm in the mindset of "If you can't beat em, join em"......and I try to get them to join in whenever we can all be on the same page........not an easy feat......
 

As for micing a cab, there's a lot of isolation boxes out there that might be able to help.  They allow you to crank the amp but they also can keep outside annoyances out.
 

 
I know of guys (including me) who have converted those weird extra closets some homes have (like under stairs) into nice iso-chambers.
 
An alternative is to soundproof the closet under the stairs and toss the kids in there, but you probably don't want to get into legal trouble...

Good idea on the closets...I got one with all sorts of clothes up on hangers..they just deaden sound!

I have a similar studio issue.  Ambient sounds from the neighborhood.
 
My studio is in an upper room of the house next to my 2 daughter's bedrooms. They are both now out of the house (one is married and both are in college) so the house is not filled with teens screaming at each other and music playing in the next room, or the TV from downstairs.
 
The studio room has sounds..... the air conditioner, while central, is still audible when it runs. In the warm afternoons, the attic ventilation fan comes on and the vibrations from it are audible as well. Then there is the computer fan, which is really pretty quiet. And then I have the traffic and the train..... that is pretty loud, especially the train and larger trucks. And of course, the occasional barking dog, or neighbor yelling.....
 
So I have to deal with that when I record anything miked. Normally, the ambient sounds are not a big issue. I simply record and let it roll. Since I do go back and listen to the vox tracks as I fix them, I get to hear anything that might have slipped onto the track. I can use audio processing to mute it or if it's in the middle of something, I simply punch in and record it a second time.
 
One of my songs has the sound of a sheet of paper my wife was laying on the floor as she worked down stairs and I was recording a vocal track directly up the stairs. It's still in the song....and if you know where, you can hear it crinkle. Easier on cans to hear it.
 
I used to take the time to edit the miked tracks going in measure by measure and using the process audio function of MUTE to carefully mute the ambient levels between the guitar or vocals. Then, one day, I realized that it really didn't make a difference that I could hear, so, unless there is something big in that track...... I let it be. I will still edit out the breaths and lip smacks and such noises because they are audible in many cases. They sound like clicks in the music BUT... I edit them as I listen to the final mix. Many times they are buried in the mix and editing then is a waste of time.  Why edit what you can't hear?
 
 
 
that's just what we have to deal with in home studios.

As I have a my own building (no not garage or a shed) for my space my only real noise issue is Trudy, who loves to curl up under the desk and snore.