TestCase (required C++11, but if replace using vector = to typedefs, behaviour is same):

#include <list>
#include <vector>
#include <cstdlib>

template <typename T>
struct VectorHolder
{
    using vector = ::std::list<T>;
};

template <>
struct VectorHolder<double>
{
    using vector = ::std::vector<double>;
};

template <typename T> using Vector = typename VectorHolder<T>::vector;

/*
 * 
 */
int main(int argc, char** argv)
{
    Vector<int> intVec;
    Vector<double> doubleVec;
    intVec. // Here methods of ::std::list resolves properly
    doubleVec. // Here NB cannot properly resolve ::std::vector methods
    return 0;
}

See screenshots.