Will my car be ok to drive on 900 mile (round trip) road trip?

I honestly think it's going to be just fine. I have a 2014 Ford Focus with the DCT transmission. The transmission sometimes lurches and vibrates but I know all about these cars and transmissions and I know it's normal for this car. It has been very reliable and I only have 13 thousand miles on it. I'm traveling to see family in Georgia from Ohio in my car and my mom is going along with me. She's concerned about the car though. Has anyone taken this car on a trip before and how was it? I mean I drove to Indianapolis in it but it was a shorter distance to drive.

You clearly already know the answer to this

When was the vehicle last serviced? Items like: tune up / oil& filter change / trans fluid and filter change / tire pressuse psi / coolant, etc etc… A good idea to have those things done before a long drive

It would have to be a total Lemon for a 2014 car not to be able to drive ~1,000 miles.

Now if you have a 10 year old car, with 100K miles on it, then you might want to get things checked over by your mechanic before the trip. But that car is still practically new, why wouldn't it drive 1,000 miles?

If you are worried that's it's 2 days continuous driving, that's not an issue. That puts LESS strain on the car than stop start driving around town. Engine is nice and warm, running smoothly, you spend most of the trip cruising in top gear. Easiest miles you can do for the car.

If it is normal then you have nothing to worry about. But it is not normal as you say. Take the car to a professional and see what they say.

You should get the transmission fixed before your warranty expires. Many Ford garages will try to downplay this, because warranty repairs don't pay like insurance work or customer pay work. There are 2 things they should do. The first thing they should do is reprogram the transmission. This will fix some of them. If it doesn't work, then they need to replace the clutch. This is a problem with the Focuses (Focusi?). Don't accept the dealer telling you it's normal. It's NOT normal and tell them you want it fixed. Tell them you're aware of the your state's lemon laws (and you should be, read up on it), and make sure they're aware that YOU'RE aware that they have 3 tries to fix the problem before they have to take the car back and return every penny you've spent on it, or replace the car with a new one. And don't be afraid to take it to another Ford dealer if the one you're dealing with now seems shady.