Smart Battery Chargers (SBCs) implementing grid-forming (GFM) control strategies are a promising solution to provide voltage and frequency support, increasing the grid reliability. Typically, GFM studies consider inverters with high DC-link capacitance. Therefore, there is a research gap in two-stage DC-AC converters with small DC-link capacitance implementing GFM strategies. This article proposes a novel approach to implement a GFM control strategy along with active power decoupling (APD) in an isolated, single-phase, electrolytic-capacitor-free two-stage DC-AC structure. The structure is composed of a voltage source inverter (VSI), DC-linked by film capacitors, with a dual-active-bridge series-resonant (DABSR) DC-DC converter. High DC-link ripple is allowed and managed by the APD. Hence, electrolytic capacitors are avoided, increasing the converter lifetime. In the proposed approach, the VSI implements the GFM strategy, operating in the four quadrants of the active and reactive power plane. However, the DABSR allows galvanic isolation, average DC-link voltage control, and suppression of the low-frequency ripple on the battery current, minimizing the impact in the battery lifetime. Design criteria are given for the DC-link voltage controller, active-reactive power controllers, inner inverter controllers, and APD technique. The control strategy is validated for vehicle-to-grid and stand-alone vehicle-to-home applications, using hardware-in-the-loop for a 2kW test setup.