We just got a puppy a month ago and work 2 miles from home. We drive to work (my husband and I work in the same office and carpool) and go home for lunch every day to eat at home and take the puppy out for a walk/play. I'm sure having the dog in the first place, and driving to and from work is not truly "mustachian" but we've had her for a month now and our entire family is absolutely besotted. The kids spend SO much more time playing with the dog instead of being online/playing video games. We go walk with her 3x per day which is great for getting us out meeting our neighbors, exercising, etc. We easily have the means to pay for the dog expenses without it really impacting our retirement schedule and I feel our quality of life has really gone up since we've had her. We'll probably cut down on our outrageous travel expenses, too, since we're not about to fly to Europe with a dog or want to leave her for long periods of time, at least not for quite awhile. I see lots of much more affordable camping in our future. ;)
In your case, if your dog walker is flexible, I think alternating days is a great idea. Cycle to work 2 or 3 days per week and have the dog walker come those days, and drive the other days so you can come home at lunch. For us, we really love going home for lunch. We actually drove before getting the dog anyway because we would run errands at lunch (without kids!), get chores done, etc. It's not the MOST mustachian approach, but going home for lunch keeps us from going out to eat for lunch, and we love going home to play with the puppy for an hour.