I'd ask a couple of follow up questions. When you are required to be away over the weekends, do you get time in lieu? A friend of mine works away over two weekends several times a year, but gets those 4 days back as lieu days. With a young baby, and assuming your wife is not working, the distinction between week days and weekends isn't as important as once they are at school.
As the job grows, what ability do you have to manage your schedule and how much is dependent on others? In one instance at the company where I worked, the person in the role was travelling almost non-stop (he was single, quite enjoyed the travel). When he left and a single mother of two took the role, the amount of travel cut back quite dramatically, but she still got the job done. She started doing video conference calls with her remote reports once a week, she planned her travel to leave Monday morning, and get back Thursday evening, meaning she was not only fully there for her kids on the weekends, she would work from home on Fridays so the weekend could start when school let out. For her long haul multi city trips, she would try and time it so again she left late Sunday (after kids had gone to bed) or Monday morning, and would take lieu days for the weekends when she got back, often tying it in to school vacations. The company was also happy for her to work extended hours when away (eg 12 hour days) and be more relaxed about when she was in town. Would your company have a similar view? I can see a trade off between travel one week, but being home by 3pm the following week, for example.