We analyze quantum phase transitions in a system of optical lattice bosons coupled to an array of atomic quantum dots. Atomic quantum dots are represented by hard-core bosons of different hyperfine species and therefore can be mapped onto pseudospins 1/2. The system parallels the Bose-Hubbard model with an additional assisted tunneling via coupling to the atomic quantum dots. We calculate the phase diagram of the combined system, numerically within the Gutzwiller ansatz and analytically using the mean-field decoupling approximation. The result of the assisted Bose-Hubbard model is that the Mott-superfluid transition still takes place; however, the Mott lobes strongly depend on the system parameters such as the detuning. One can even reverse the usual hierarchy of the lobes with the first lobe becoming the smallest. The phase transition in the bosonic subsystem is accompanied by a magnetization rotation in the pseudospin subsystem with the tilting angle being an effective order parameter. When direct tunneling is taken into account, the Mott lobes can be made to disappear and the bosonic subsystem becomes superfluid throughout.