OK, I say go get your hair done somewhere else. Why? becauses it is something different. It may shake the boat a bit. Don't talk about it, just do it. Don't mention it to her before or after, just go get your hair cut. See what happens. IF you get a good reaction, cool, if you get a bad reaction you can always have her do your hair next time. NOW that said, you are over thinking stuff a bit. This is common for the newbie. A hair cut will not make or break your marriage. So do what you want. She might also seem pissed you got your hair cut somewhere else but that pissed may actually work in your favor. So many factors, so much to consider BUT a strong, confident, man with options wouldn't sweat it either way, he would do what he wants. Always remember, "What would Ron Burgundy do?"
Now as far as giving space goes, you can give space and still be in the house, just stop puppy dogging her if you are doing that, try to not seem sad or peeved. DO NOT have any R talks. Again, live your life like it is all good. Do stuff with the kids. Fix stuff around the house. Things like that. BTW, it is all easier said than done. I dunno about the others here but I still have to conciously work on all this stuff everyday.
Me 44 She 46 S13 D9 M18 T23 3 years DB'ing Successfully busted