How to use mapper.Map inside MapperConfiguration of AutoMapper?

As of AutoMapper 8.0 and up
The answer below for 5.1.1 still applies, but note that the use of ResolveUsing has been replaced with an overload of MapFrom, but the signature has otherwise remained consistent.

As of AutoMapper 5.1.1

You can get to the mapper using another overload of ResolveUsing with four parameters, fourth of which is ResolutionContext (context.Mapper):

var config = new MapperConfiguration(
    cfg => {
        cfg.CreateMap<Customer, CustomerDto>();
        cfg.CreateMap<Customer, DetailedCustomerDto>();
        cfg.CreateMap<Order, OrderDto>()
             .ForMember(dst => dst.Customer, src => src.ResolveUsing((order, orderDto, i, context) => {
                return order.Type == 1
                ? context.Mapper.Map<Customer, CustomerDto>(order.Customer)
                : context.Mapper.Map<Customer, DetailedCustomerDto>(order.Customer);
        }));
 });

 var orderTypeOne = new Order();
 orderTypeOne.Type = 1;
 orderTypeOne.Customer = new Customer() {
    Id = 1
 };

 var dto = config.CreateMapper().Map<Order, OrderDto>(orderTypeOne);
 Debug.Assert(dto.Customer.GetType() == typeof (CustomerDto));

 var orderTypeTwo = new Order();
 orderTypeTwo.Type = 2;
 orderTypeTwo.Customer = new Customer() {
     Id = 1
 };
 dto = config.CreateMapper().Map<Order, OrderDto>(orderTypeTwo);
 Debug.Assert(dto.Customer.GetType() == typeof (DetailedCustomerDto));

Prior to AutoMapper 5.1.1

You can get to the mapper using another overload of ResolveUsing with two parameters, first of which is ResolutionResult (result.Context.Engine.Mapper):

var config = new MapperConfiguration(
    cfg => {
        cfg.CreateMap<Customer, CustomerDto>();
        cfg.CreateMap<Customer, DetailedCustomerDto>();
        cfg.CreateMap<Order, OrderDto>()
             .ForMember(dst => dst.Customer, src => src.ResolveUsing((result, order) => {
                return order.Type == 1
                ? result.Context.Engine.Mapper.Map<Customer, CustomerDto>(order.Customer)
                : result.Context.Engine.Mapper.Map<Customer, DetailedCustomerDto>(order.Customer);
        }));
 });

 var orderTypeOne = new Order();
 orderTypeOne.Type = 1;
 orderTypeOne.Customer = new Customer() {
    Id = 1
 };

 var dto = config.CreateMapper().Map<Order, OrderDto>(orderTypeOne);
 Debug.Assert(dto.Customer.GetType() == typeof (CustomerDto));

 var orderTypeTwo = new Order();
 orderTypeTwo.Type = 2;
 orderTypeTwo.Customer = new Customer() {
     Id = 1
 };
 dto = config.CreateMapper().Map<Order, OrderDto>(orderTypeTwo);
 Debug.Assert(dto.Customer.GetType() == typeof (DetailedCustomerDto));