In response to the challenges of low-carbon operation in distribution networks and to fully exploit the flexible regulation potential of distributed resources, a bi-level peer-to-peer (P2P) trading model for virtual power plants (VPPs) based on integrated electricity-carbon marginal pricing is developed. In the upper level, a carbon-aware optimal power flow model based on carbon emission flow (CEF) technology is established by the distribution system operator (DSO). An integrated electricity-carbon marginal price is calculated, which is used by the DSO to coordinate low-carbon scheduling of VPPs. In the lower level, a multi-VPP coalition is formed to aggregate electric vehicles (EVs) at scale. A flexible EV scheduling mechanism guided by carbon signals is introduced. An asymmetric Nash bargaining model based on contribution degrees is constructed, where VPPs balance individual and coalition interests under price signals to determine optimal production and trading strategies. The model is solved by the adaptive-scaling alternating direction method of multipliers (AS-ADMM) to address convergence issues caused by variable coupling. Finally, simulation verification is carried out on a modified IEEE 33-bus distribution system. Case study results show that the proposed trading model reduces VPP operating costs and lowers carbon emissions of the distribution network by improving distributed energy utilization and optimizing load distribution.