Boy, are you in a pickle. I sympathize. You're trying your hardest to protect your dad, but dealing with contradictory medical advice. Not to mention your dad's stubbornness about getting and family stress. I noticed your email name is "worn out," and I can see why.
outside help. There are different ways of looking at this. One is to let your dad do as he chooses as it's his life. The other is to dig-in as the caring offspring, and do all you can for his health, safety,
First, I would talk to all of your dad's doctors about how the contradictory advice on his ability to travel is extremely stressful on you (and the family), and ask if they can reach consensus. They may not be used to this kind of request, but it's worth a try. If they're not able to agree (and many time doctors do come to different reasonable conclusions), I'd err on the advice of the cardiologist or heart doctor, as this is your dad's most serious concern. I'd ask the cardiologist for specific details on why he/she thinks your dad should or shouldn't travel, and write them down, so you can discuss them with your dad and other family members. If the doctor thinks it's safe for your dad to travel, be sure to ask for tips or pointers on making the trip comfortable and successful. If the doctor thinks it's not safe, ask for details on the risks, so you can point them out to your dad.
You can also try asking the doctor to talk to your dad about the importance of getting outside (nonfamily) assistance, as his family is maxed out. He may better "hear" this if it's coming from a medical expert.
A few other things to consider: Maybe your dad would be open to a friend or family traveling companion, like a teen or young adult. An informal caregiver. Or part-time assistance, that comes across to him as no big deal.
If he doesn't budge, it's really OK for you to practice tough love. You and other family members can lay your concerns on the line. "Plain talk," is hard to do. But it really can make a difference, especially if it's spoken calmly, without anger. "Dad, I love you dearly, and this is my bottom line. . . "