Hi Jimbo. i have a cheap Android phone that I use for regular phone service in the US. I have the Google Voice app installed. This gives me a second US phone number associated with the Google Voice app, I can make free calls to US numbers, including landlines. It will work to make or receive calls even if I have only WiFi and no phone service, though I first needed service with this phone in order for Google to let me use the Google Voice app to make or receive calls.
I use Google Voice for almost all of my regular calls even in the US and for texting too. When I got to Europe, I use a Dutch Vodafone SIM for data, and I make and receive calls with my phone just as in the US. No one calling me would know whether I am in Europe or in the room next to them when they call my Google number.
So your situation is a bit complicated since your phone with regular service is a flip phone (can't install the Google Voice app), and your smart phone doesn't have regular phone service. I don't think you'll be able to set up Google Voice on it without service, and Google may not work well with a Tracfone device at least while trying to set up the app the first time.
If your smart phone will work on Verizon's network, you could move your Verizon SIM over to the smart phone temporarily, install Google Voice on the smart phone, let it associate your Google account with your Verizon number...and then move the Verizon SIM back to the flip phone. Google Voice should continue to work for making and receiving calls after that. I'm not sure how it will continue to work after you put the Tracfone SIM back in, but you can try this - it won't cost you anything. If you can put the smart phone in airplane mode, then turn on WiFi, then call your parents with the Google Voice app, then it should work that way in Europe, too. Your parents should be able to call you also.
If this sounds too complicated, you could set up Skype on the smart phone and buy some credit - $10 blocks I think. This would let you make cheap calls to US numbers for a cents a minute. You could also buy a US phone number with Skype for a few months, just before you go to Europe, to receive calls in Skype too. But...the smart phone would need some sort of internet service - WiFi, a SIM for mobile data, whatever - while in Europe to be able to make or receive calls. If it's OK just to use Skype to call home (parents can receive calls from it on their landline) say when you are at your hotel or at a restaurant with WiFi, then that might work OK and not cost much. You wouldn't have to mess with SIM cards or even remove the Tracfone SIM, though I don't think it would work in Europe.
If you are able to get an eSIM to work with your smart phone to have service in Europe, so you can use it even without WiFi, then either Skype or Google Voice might work.
Of course, you could just pay Verizon's international roaming fee and use the flip phone in Europe...assuming your PHONE itself will work in Europe. Have you used it there before? Don't assume it has all of the necessary frequencies to work in Europe - some phones don't even if they work fine in the US.