I've been in your position. A couple of times. You are lucky that you travel a lot. It means that you can justify time out of the office.
I try to schedule job interviews as late in the day as possible. Several job interviews have taken place at 5:00 or later. A good employer understands that you at at your job all day. The other thing this helps with, you get to see what your commute home would be like at rush hour. I left an interview a 5:30 and got stuck in a terrible traffic mess. They offered the next day but I turned it down, based partly on the ride home. I didn't want to go through that every day.
The same can be said about interviews first thing in the morning. FInd out what the drive is like.
Being newly married can b to your benifit. If you need to take off in the morning or afternoon, you can use some newlywed excuse, like my wife and I have to...sign papers, go to a bank, whatever. Saying that, I'm not sure your boss can quiz you on what you are doing. You might justsay, I have to take care of some personnel business and leave it at that. Several years back, when the economy was great, I job hopped like everyone else. I took off at 2:00 every afternoon for a week. The boss came to me on Friday and asked if everything was ok, and I just said I was taking care of some personnel business.
Being on the road is great. If you can schedule an interview near wear you are going to be, try to do it areound lunch. If anyone asks where you were, just say lunch. I've done that too. (Changing into interview clothes in the back of a truck wasn't much fun).
If you don't have a cell phone, you may want to get one, maybe short term, so you can get calls away from the office.
Good Luck.