I would not recommend driving to Lisbon for a day trip.
Although it will only take you about 2hrs:45mins, getting into the centre of Lisbon can be a pain as can be finding parking.
There are regular trains from Faro via Loulé Station ( on the old road from Quarteira to Loulé ) to Lisbon Entrecampos. (nearest station to Vilamoura).
There is an Alfa-Pendular from Loulé daily at 7h06 arriving Lisbon Entrecampos at 9h56.
Until the end of September (summer timetable) there are return departures as follows:
Lisbon Entrecampos 18h51 Loulé 21h44 2h53
Lisbon Entrecampos 19h30 Loulé 23h09 3h39
From Entrecampos I would recommend either a taxi or Metro(change at Pombal) to Rossio in the baixa, the old centre of Lisbon.
The above should give you at least 8 hours in Lisbon. (Delays withstanding)
You will be more relaxed. There are good on-board cafes on the train and you will have a great view of the Tejo and Lisbon going north as you come out of the tunnel just after Pragal station.
