Driven by carbon-neutral targets and transportation electrification, the widespread use of electric vehicles (EVs) has become an irreversible trend. However, low-voltage distribution networks (LVDNs) can face several challenges under the high-penetration EV integration, including overloads, voltage violations and unbalance issues. In this paper, an EV integration-oriented DC conversion scheme and the associated adaptive control method for LVDNs is proposed, aiming at releasing more capacity for EVs and collaborative improvement of the above issues caused by EV charging. Based on analyzing the influence of different charging piles connected to the AC and DC LVDNs, a DC conversion scheme for three-phase four-wire LVDNs under high-penetration EVs is proposed. The voltage source converter (VSC) control strategies aimed at alleviating the overload of the DTs, voltage violations, and three-phase unbalance are designed separately based on the modified three-phase four-wire voltage sensitivity. Then, a coordinated adaptive control strategy of on-load tap changer and VSCs is proposed considering the simultaneous occurrence of multiple power quality issues in hybrid AC/DC LVDNs. Case study verifies the effectiveness of the proposed DC conversion and adaptive control methods, by which the maximum EV penetration of the hybrid AC/DC LVDN is increased from 85% to 215% compared with the AC LVDN.