Inspired by recent developments in the control and manipulation of quantum dot nuclear spins, which allow for the transfer of an electron spin state to the surrounding nuclear-spin ensemble for storage, we propose a quantum repeater scheme that combines individual quantum dot electron spins and nuclear-spin ensembles, which serve as spin-photon interfaces and quantum memories respectively. We consider the use of low-strain quantum dots embedded in high-cooperativity optical microcavities. Quantum dot nuclear-spin ensembles allow for the long-term storage of entangled states, and heralded entanglement swapping is performed using cavity-assisted gates. We highlight the advances in quantum dot technologies required to realize our quantum repeater scheme which promises the establishment of high-fidelity entanglement over long distances with a distribution rate exceeding that of the direct transmission of photons.