Is it considered a correct action for a person not to travel to attend a relative's wedding due to their certainty that it will involve musical instruments and dancing, and instead to suffice with congratulations, a phone call, and sending a sum of money?

All praise is due to Allah, and peace and blessings be upon the Messenger of Allah, and upon his family and companions. To proceed:

You did well by not attending the wedding that included reprehensible acts such as musical instruments, based on the words of Allah Almighty: "And He has already sent down to you in the Book that when you hear the verses of Allah disbelieved in and scoffed at, then do not sit with them until they enter into another conversation. Indeed, you would then be like them" (An-Nisa: 140). First, you should enjoin them from evil. If they do not respond, then avoid witnessing the evil.

And Allah knows best.