I [40M] began working from home to save the commute, but my wife [43F] won't let me work in peace!

Hi Dating.mobi, I appreciate your help.
I'm a graphic designer and up until a month ago I worked in a corporate office downtown. The commute there always ate up more than an hour each way, and it was draining. My boss looked over my responsibilities and together we agreed that, if I wanted, I could work from home for four days of the week, and check in at the main office only on Mondays for our weekly team meetings and other sundry office tasks. Such a schedule would allow me to take the metro or even a bus to work on Monday, as our team meetings didn't start until later. My boss did mention that it would entail a small pay cut, due to my not being present for certain tasks. I talked it over with my wife that night, and although she didn't like the pay cut (it was about 10%) she agreed with me that the gasoline, and to say nothing of my time, would make up for it.
So, I began my home office career. My wife and I started our family later in life, and have a four year old daughter daughter. We live in a two and a half bedroom apartment, the "half" previously having been our child's playroom. I thought this might be an issue, but my wife assured me that our daughter can just play in the main living room during the day, or in her own room, and that anyway she will be in preschool in the fall. My wife is a stay at home mom but we've agreed that when our daughter starts kindergarten or first grade, she can return to office assistant work, which is what she did previously, or finish her bachelors degree in English at an accelerated pace, which she had been steadily working on for several years.
Now that I work at home, I put myself on a strict schedule. I start at 9am, and complete all the tasks that I can before 5:30pm, which is when the downtown office closes. I give myself two, fifteen minute coffee breaks (going to the bathroom doesn't count as a break, LOL), and one hour for lunch, just like I had at the downtown office. The rest of the time, I am at my computer working. This compares very favorably to my previous schedule, but involved me waking up at 6am to shower and dress in the morning, and me showing up exhausted at home around 8 o'clock at night. Now I just waltz into my workspace in my house clothes, unless I'm doing face-time with coworkers or the boss, where in which case I will dress more respectfully.
All this sounds really convenient, but right away, my wife seems to think that the fact that I'm home means that I am on vacation and have endless free time on my hands. She will constantly interrupt me and want me to take walks with her, our child, and our dog (I forgot to mention we have a pug). I tell her, why not wait until 10:30am when I have a break? Or that, since I'm taking my break early, I can't take another one when she interrupts me yet again later. Or I tell her that I am in the middle of something, but she thinks I am just being mean. I certainly spend my lunch hour with her and my child, but oftentimes my wife will assume that I can just blow off work because I "just work in front of a computer anyway" and that I can just "catch up with work later," as if my job is so easy.
I know she means well but she seems to believe that my work is easy or not a real job (even though it pays for the roof, lights, food, and everything else) and that I can just "phone it in" and no one will notice. She has actually barged into my office with the kid asking us to go out shopping when I was on a tele-meeting with my boss. And although my boss has met her before and is friendly, and gave all the polite niceties to an employee's spouse, after she left, I could tell he was annoyed. Since then I've taken to locking the door during my meetings and telling my wife ahead of time when it was important for her to help our child be less fussy during those times, sure enough, whenever I have a meeting my wife or my daughter will be banging on the door asking for me to come out and play.
I love my wife and I know she thinks she isn't being disrespectful or bad, but any advice on how to deal with this situation? Honestly the home office has saved a lot of stress, but the constant interruptions are stressful too, to the point where I'm starting to fall behind! Advice is appreciated.
**tl;dr: I work in a home office. My wife will not leave me alone!**


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