Driving through spain

Check to see what drop-off fees are in Gibraltar, could be expensive as it’s a foreign country to Spain.

If you wish to end in Gibraltar, drop the car at the Spanish town the borders Gibraltar. I believe the town is La linea. Walk across to your destination.

Ensure you will have driving permission.

Security advice for Spain from German Ministry for Foreign Affairs:
"Along Spanish highways (especially on the A7 between the French-Spanish border station La Jonquera and Barcelona, but also further along), tourists are often targeted in robberies. The victims are approached by one or two vehicles driving alongside them, often with German or other foreign license plates, who honk their horns or throw stones at supposed or actual damage to the vehicle (e.g., deliberately caused flat tires) and offer “assistance”.

Do not stop on the hard shoulder; continue driving to the nearest gas station or busy rest stop. Call the emergency number 112 and describe the incident.

When visiting the nearest gas station, rest stop, or parking lot, do not leave any visible valuables in the vehicle and lock the vehicle—even if there are two of you."

Translated with DeepL.com (free version)

As previously stated, you will almost certainly be required to drop the car in an underground parking garage in La Linea which has an arrangement with the major rental companies.
The rental companies have small desks/office either at the airport or in La Linea near the border.
From the carpark it is a five/ten minute walk to the border and the airport.
Is there a reason you want to drop the car in Gib?
It will mean backtracking from Seville.

En route, Tarragona and Cartagena are worth a one night stop. Malaga two nights.

I lived near Gibraltar for 12 years, and have done the Barcelona/Gib drive you are planning and also often from Gib to Seville and beyond. Never heard of the attacks described. Of course, things might have changed since then.

Just looked up the foreign travel advice for Spain from UK gov with similar warning, see "Vehicle crime".

I understand the "vehicle crime" discussion, but we drove extensively in Spain this summer and saw absolutely no evidence of elevated risk. Spanish roads were quite good, and fuel was significantly cheaper than in France. Spain was a revelation to us, as the economy is jumping and lots of construction is underway.