I have never had the issue. I would guess that part of it would be which way I was traveling.
For example, if my diocese celebrated the holy day on, say, Thursday, but I am leaving on a Wednesday, and the other diocese celebrated it on Sunday, but I was returning on Friday, and assuming I knew all of this, I would simply speak to my pastor about missing the day and request permission. And it would be an unusual priest who would not give it.
With the reverse, if I knew I would be back in my diocese to celebrate it on that coming Sunday, then it would be optional as to whether or not I went to Mass on that Thursday, I believe, as I am not a resident of the diocese holding to the weekday, and so am not bound by their determination. Certainly there would be no problem attending on Thursday even though I would be returning for the Sunday celebration.
And if the first scenario occurred but I was not aware of the difference, I have committed no sin. I am not intentionally missing the celebration.