This is just unconditional speculation, but the standard TSP tends to benefit from operators who try to preserve the adjacency of nodes in parent tours. So it’s important not that the city X appears in a certain position, but instead it appears next to the cities Y and Z, wherever they appear in the line. There are operators such as Edge Assembly Crossover (EAX) that have been specifically designed to try to use this structure.
In your case, time windows presumably mean that, unlike TSP, tours like 01234567 are different from tours like 56701234, and so the absolute position of the city on the tour also matters. In situations like QAP, where absolute position is important, people tend to do things like Cycle Crossover (CX).
If I were committed to GA for this problem, I could start by doing something obvious, how to implement both CX and EAX, and choose between them at random. Alternatively, you can try to create a single hybrid operator combining the elements of both, but this is probably pretty nontrivial.
I suspect, however, that GA cannot be here, or at least the GA black box may suffer. An operator trying to use semantic information from an instance of a problem, for example, tends to group cities next to each other if they have the same time windows that can be effective. And my 5 US dollars say that a good local search algorithm (taboo search, search by variable neighborhoods, etc.) can beat GA anyway, although this is based on nothing more than a hunch.
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