Is a day trip reasonable?, any companies you could recommend?, we'll have a car and could drive if a better option.
If you only have 4 days allocated to Rome and haven't been there before, I would skip Pompeii. The ancient town of Ostia Antica is only 30 minutes from Rome via train, easier & has much of the splendor, though not the catastrophic impact, on a smaller area. Save yourself the incredible aggravation & hassle of a car, you don't need it or certainly want one in Rome, or south to Naples & on to Pompeii. It's not a great area for driving and trains are reliable & much easier.
A day trip to Pompeii from Rome is possible, but a very long day and if you have more time, choose to spend it either in Naples so you can eat some great food & visit the magnificent Archeological Museum (need to book in advance) or in Sorrento because it's a good jumping off point for Pompeii and some people like the more relaxed vibe. LOTS on the forum, use the search bar above in addition to the excellent ideas given above. Good luck.