I would do Figueres the first thing in the morning and head back to Girona for lunch (1:30 - 4:00) with a visit to the old city. There is a Regional departing at 08:25, which would put you in Figueres at 10:44. The cost is 8.55 euros, one-way.

Renting a car for one day would be impractical.

I'd suggest you try and get an earlier train if you can, as you may have to queue to get in to Dalí Museum and then you are really cutting short the time left for Girona, and Girona deserves more than a couple of hours.

There's a Catalunya Express (costs 9.80€ single to Figueres) leaves BCN_Sants at 7.46 ,or 7.50 at Passeig de Gracia (Renfe station, next to metro, entrance at Atragó corner by Casa Batlló). That runs Mon-Fri and gets into Figueres at 9.30.

At weekends you'd have to use more expensive Tren Estrella "Costa Brava" which runs from Madrid to Cerbere in France (15.30€ single); arrives Sants 7.35, leaves 7.52 and gets into Figueres at 9.57. Note that this train stops only at Sants. Obviously if you are staying in the centre, Passeig de Gracia is almost certainly more convenient ie Catalunya Express is better.

Trains from Figueres to Girona at 12.03,12.39, 14.02 (ie 2.02pm), 14.31 (2.31pm). Timetables on www.renfe.es