Tidal dwarf galaxies (TDGs) are low-mass objects that form within tidal and/or collisional debris ejected from more massive interacting galaxies. We use CO(1 - 0) observations from ALMA and integral-field spectroscopy from MUSE to study molecular and ionized gas in three TDGs: two around the collisional galaxy NGC 5291 and one in the late-stage merger NGC 7252. The CO and Hα emission is more compact than the H I emission and displaced from the H I dynamical center, so these gas phases cannot be used to study the internal dynamics of TDGs. We use CO, H I, and Hα data to measure the surface densities of molecular gas (Σ_mol), atomic gas (Σ_atom) and star-formation rate (Σ_SFR), respectively. We confirm that TDGs follow the same spatially integrated Σ_SFR - Σ_gas relation of regular galaxies, where Σ_gas = Σ_mol + Σ_atom, even though they are H I dominated. We find a more complex behaviour in terms of the spatially resolved Σ_SFR - Σ_mol relation on sub-kpc scales. The majority ($\sim {60\%}$) of SF regions in TDGs lie on the same Σ_SFR - Σ_mol relation of normal spiral galaxies but show a higher dispersion around the mean. The remaining fraction of SF regions ($\sim {40\%}$) lie in the starburst region and are associated with the formation of massive super star clusters, as shown by Hubble Space Telescope images. We conclude that the local SF activity in TDGs proceeds in a hybrid fashion, with some regions comparable to normal spiral galaxies and others to extreme starbursts.