Force on a Magnetic Dipole due to Another Dipole

I’m trying to find the force on a magnetic dipole $m_2(r,0,0)$ on the x-axis due to the magnetic field $vec B_1$ produced by a another dipole $m_1(0,0,0)$ which is at the origin. Both magnetic points $vec m_1$ and $vec m_2$ point in the positive x-direction

I’ve made the assumption that a dipole can be modelled as a small current loop and therefore has the field:

$$vec B_1 = mu_0 frac {m_1}{4pi r^3} (2cos theta hat r + sin theta hat theta)$$

The formula to find the force is $vec F = nabla(vec m cdot vec B)$, now in order to use this I decided to convert $vec B_1$ into cartesian coordinates using:
$$hat r = sin theta cos theta hat x +sin theta sin phi hat y + cos theta hat z $$
$$hat theta = cos theta cos phi hat x + cos theta sin phi hat y – sin theta hat z$$

Since I’m looking for $vec m_2 cdot vec B_1$ and $vec m_2 = m_2 hat x$ only $B_x$ is relevant which using the conversion I found to be: $B_x = mu_0 frac {m_1}{4pi r^3} (2cos theta (sin theta cos phi) + sin theta (cos theta cos phi)) = 3mu_0 frac {m_1}{4pi r^3} sin theta cos theta cos phi$

Now from here I get unsure of how to continue, do I take the Cartesian Gradient or Spherical? I would think Cartesian since I did the scalar product in Cartesian. But since I don’t have a function of $x, y$ or $z$ this would yield $0$. Using the Spherical Polar Gradient I get a large expression which I don’t believe is correct:
$$vec F_{21} = mu_0 frac {m_1m_2} {4pi r^4} (-9 sin theta cos theta cos phi hat r + 3cos phi cos2 theta hat theta + -3cos theta sin phi hat phi)$$
Using a different formula Forces between two magnetic dipoles I get:
$$vec F_{21} = -3mu_0 frac {m_1m_2} {2pi r^4} hat x$$
Which looks more correct since it is almost identical to a result from Griffith’s which deals with a similar problem but with the two dipoles on the z-axis. I would appreciate it if someone could help me figure out what is wrong with my original approach. I know I can get the right answer just using the formula but I would really like to know why the first one doesn’t work.

EDIT:

I’ve realised the reason why the method does not work is because the expression for $vec B_1$ I was using was only valid for a dipole with a magnetic moment orientated in the positive $hat z$ direction.