This decision becomes much easier once you stop comparing the two roles on salary alone.
McKinsey would give you substantially higher compensation, a steeper learning curve, broader exposure, and potentially stronger exit opportunities. But you are being paid partly because you are giving up something valuable: control over your time. Frequent travel plus long client days can materially change how much time and energy you have available for your spouse and life outside work.
I would also remove the assumption that your wife can routinely travel with you. Even when logistics allow it, being in the same city does not mean you will have meaningful time together. Your schedule will be driven by the client and team, not by the fact that your spouse is nearby.
The right question is what you are optimizing for over the next two or three years. If you specifically want the training, brand, network, and career acceleration, accepting a temporary lifestyle sacrifice can be rational. If you mainly want the additional income for a house, there may be easier ways to increase your earnings without changing your entire lifestyle.
Before continuing, talk through a realistic week with your wife: when you leave, when you return, how often plans change, and what happens if you have children earlier than expected. Make the decision based on that version of the job, not the best-case version.