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The brightest cluster galaxies in the cooling clusters A1664 and A1835 both harbour more than 10 billion solar masses of molecular gas and nuclear starbursts at levels not seen except in the early Universe. The molecular gas, which probably formed from hot gas cooling out of the clusters' X-ray atmospheres, may be fuelling the powerful AGN outbursts observed as expanding radio bubbles, shocks and gas outflows. I will discuss our ALMA Early Science observations of these relatively nearby systems which show the bulk of the molecular gas is centrally condensed and spatially coincident with the star formation. In A1664, extended molecular gas filaments trace low temperature X-ray and Halpha-emitting material, which could mark residual cooling from the hot atmosphere. The CO(3-2) velocity map shows a rotating molecular disk, potentially fuelling the AGN, and a spectacular ~10 billion solar mass filament projected across the nucleus at ~600km/s with respect to the systemic speed. This gas was either ejected from the nucleus by the AGN or is falling onto the system at high speed. In A1835, we also observe molecular filaments drawn up around the northern radio bubble suggesting for the first time that radio jets interact with the cold, dense molecular gas as well as the hot, diffuse intracluster medium.