We present, for the first time, numerical simulations of young tidal dwarf galaxies (TDGs), including a self-consistent treatment of the tidal arm in which they are embedded. Thereby, we do not rely on idealized initial conditions, as the initial data of the presented simulation emerge from a galaxy interaction simulation. By comparing models which are either embedded in or isolated from the tidal arm, we demonstrate its importance on the evolution of TDGs, as additional source of gas which can be accreted and is available for subsequent conversion into stars. During the initial collapse of the proto-TDG, with a duration of a few 100 Myr, the evolution of the embedded and isolated TDGs is indistinguishable. Significant differences appear after the collapse has halted and the further evolution is dominated by the possible accretion of material from the surroundings of the TDGs. The inclusion of the tidal arm in the simulation of TDGs results in roughly a doubling of the gas mass (Mgas) and gas fraction (fgas), an increase in stellar mass by a factor of 1.5 and an approximately three times higher star formation rate compared to the isolated case. Moreover, we perform a parametric study on the influence of different environmental effects, i.e. the tidal field and ram pressure. Due to the orbit of the chosen initial conditions, no clear impact of the environmental effects on the evolution of TDG candidates can be found.