Overall enthalpy balance on a mixing process
Let’s use a trivial case to test the two possible results. If we set $T_\ce{A}$, $T_\ce{B}$, and $T_p$ all to room temperature, the first and third term would be zero (sign does not matter), and you should simply get the enthalpy of mixing as a result. The result you arrived at does that, but the answer you were given changes the sign.

Unless there are some unexpected conventions about the signs of the terms, your result makes more sense.