Given the additional constraint that the coefficient of $x^4$ in each polynomial basis vector must be -2000, we need to adjust our basis vectors accordingly. Let's construct the basis:

We start by ensuring that each polynomial $p(x)$ in the basis satisfies $p(1) = p'(1) = 0$ and the coefficient of $x^4$ is -2000.

Consider the following basis vectors:

1. $p_1(x) = -2000(x-1)^2 x$
2. $p_2(x) = -2000(x-1)^3 x$
3. $p_3(x) = -2000(x-1)^2 x^2$

These polynomials satisfy the conditions $p(1) = p'(1) = 0$, and the coefficient of $x^4$ is -2000 in each case.

Therefore, the basis $B$ is:

$B = \{ -2000(x-1)^2 x, -2000(x-1)^3 x, -2000(x-1)^2 x^2 \}$