Should my mom and step dad borrow my new car?

So I just got a slightly used 2010 hyudai sonata, fully loaded, approximately 5 months ago. I have also temporarily moved back home after being on my own for 10 years. I drove my car from the West coast to the East coast as this once in a life time deal. My mom and step dad’s plan to take their older car with known problems out to the West coast undoubtedly fell through. So guess whose car they want to use? They have been overwhelming supportive of me through my late teens into adulthood. I am living with them rent free while I look for work. So, am I being selfish in not wanting them to take my brand new car BACK across the country?? My mom is miffed about my refusal and it’s making for tense living curently. I appreciate your thoughtful feedback.