Car Rental Recommendations and/or best best transportation options from Barcelona to Begur

Hello!
My family of 5 (3 kids-13,11 & 7 yrs. old) will be staying 4 nights in Barcelona (7/27-30) before heading up to Begur (7/31-8/3) for 3 nights. Originally I was looking to rent a car for the later part of the trip (7/31) from downtown Barcelona (we are staying near the Passeig de Gracia metro station on Carrer de Pau Claris), drive out of the city in the morning and stop at Tossa de Mar for lunch mid day before heading up to Begur.
Although there are rental car companies nearby, I've read a bunch of bad reviews for almost all of them. Some people have recommended renting outside of Barcelona, as it is hard to get out of the city center and thieves target tourists and rental cars by slashing tires at traffic stops. I would really like to have a rental car option as we plan on a day out at Pals and driving between some of the nearby coastal towns from Begur during our stay up in the Costa Brava.
My questions are:
1. How bad is the traffic, roads getting out of the city and how often do these tire slashing happen? My husband will be driving, and he is a good driver, used to NYC traffic for work and the roundabouts in NJ where we live. I've read from terrible to not so bad, so I'm thinking we can handle it. The tire slashings, I read are common in July when the tourists come in and are followed out pretty much from the rental car locations. Reviews have said that the rental companies have been slow, indifferent and overcharging a lot in these instances.
2. If it is not recommended to rent a car from downtown Barcelona, how far out should one go out? There are some locations for Enterprise at the Glories location if it's worth it? Is that far out enough, and thus easier to get onto the major roads?
3. If car rentals and driving from Barcelona is a hassle, would it be worth it to take the train up to Girona and rent a car from there? We would still have about an hour drive to Begur after the train ride, and would have to cancel stopping by Tossa de Mar on the way up.
4. I've looked into bus options too, but from the biggest town close to Begur (Palafrugell) there does not seem to be available car rentals for a family of 5 this close to the trip and peak season.
5. Lastly, if we are going to rent a car from Barcelona (most likely?), which are the most decent ones downtown? Granted each one has had their horror story in reviews, but trying to find the best out of the worst. We will go for the basic protection plan as I heard a lot of places make a big fuss over this, get super rude and difficult, and a local friend who is from Barcelona told me to just get it, as something has always happened to her car rentals whenever she visited and used one.
Sixt is out of our price range ($670-755 for 4 days w/ CDW). EuropCar has options from $558-596 with same days and protection, while Enterprise comes in at $449.55 and Avis at $486. My husband is a Hertz Gold member, but they are not as centrally located or in the opposite direction of where we are heading out, and reviews still have horror stories for Gold members regardless. I'm leaning towards Enterprise and Avis, or might splurge on EuropCar for a little peace of mind (though that is the location of the tire slashings I read about on TripAdvisor, but EuropCar seems to have overall better reviews than Enterprise and Avis)
Thank you for any feedback- I would appreciate hearing from anyone who has done this somewhat recently, as well as during the peak summer season. I know I sound paranoid and my husband thinks I am totally overthinking this, but from my experience the worst always happens when you assume all will go well!
Best, Judy