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 Atacama Large Millimeter/submillimeter Array and integral-field spectroscopy from Multi-Unit Spectroscopic Explorer to study molecular and ionized gas in three TDGs: two around the collisional galaxy NGC5291 and one in the late-stage merger NGC7252. The CO and H alpha emission is more compact than the Hi emission and displaced from the Hi dynamical centre, so these gas phases cannot be used to study the internal dynamics of TDGs. We use CO, Hi, and H alpha data to measure the surface densities of molecular gas (Sigma(mol)), atomic gas (Sigma(atom)), and star formation rate (Sigma(SFR)), respectively. We confirm that TDGs follow the same spatially integrated Sigma(SFR)-Sigma(gas) relation of regular galaxies, where Sigma(gas) = Sigma(mol) + Sigma(atom), even though they are Hi dominated. We find a more complex behaviour in terms of the spatially resolved Sigma(SFR)-Sigma(mol) relation on subkpc scales. The majority (similar to 60 per cent) of star-forming regions in TDGs lie on the same Sigma(SFR)-Sigma(mol) relation of normal spiral galaxies but show a higher dispersion around the mean. The remaining fraction of star-forming regions (similar to 40 per cent) 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 star formation activity in TDGs proceeds in a hybrid fashion, with some regions comparable to normal spiral galaxies and others to extreme starbursts.