The ultraluminous infrared galaxy F13451+1232 is an excellent example of a galaxy merger in the early stages of active galactic nucleus (AGN) activity, a phase in which AGN-driven outflows are expected to be particularly important. However, previous observations have determined that the mass outflow rates of the warm ionized and neutral gas phases in F13451+1232 are relatively modest, and there has been no robust detection of molecular outflows. Using high-spatial resolution Atacama Large Millimeter/submillimeter Array CO(1-0) observations, we detect a kiloparsec-scale circumnuclear disc, as well as extended (r ~ 440 pc), intermediate-velocity (300 < |v| < 400 km s-1) cold molecular gas emission that cannot be explained by rotational disc motions. If interpreted as AGN-driven outflows, the mass outflow rates associated with this intermediate-velocity gas are relatively modest ($\dot{M}_\mathrm{out}=22$-27 M⊙ yr-1); however, we also detect a compact (rout < 120 pc), high-velocity (400 < v < 680 km s-1) cold molecular outflow near the primary nucleus of F13451+1232, which carries an order of magnitude more mass ($\dot{M}_\mathrm{out}$ ~ 230 M⊙ yr-1) than (and several times the kinetic power of) the previously detected warmer phases. Moreover, the similar spatial scales of this compact outflow and the radio structure indicate that it is likely accelerated by the small-scale (r ~ 130 pc) AGN jet in the primary nucleus of F13451+1232. Considering the compactness of the nuclear outflow and intermediate-velocity non-rotating gas that we detect, we argue that high-spatial resolution observations are necessary to properly quantify the properties of AGN-driven outflows and their impacts on host galaxies.