Hey Tony,
chatter is unlikely to come from the spindle – at least if it is a real spindle (a frequency-controlled three-phase induction motor) that hangs on a good VFD. If you use a spindle with 2.2 kW mechanical power at the shaft, and two magnetic poles which means about 0.9 Nm @ 24,000 rpm @ 400 Hz, and you have chatter, usually it’s the CNC machine that is the weak spot (unless you exaggerated with some cutting parameters).
You say “2 HP” spindle but be careful, some chinese manufacturers write e.g. “2.2 kW” on their spindle but do not mean the mechanical power available at the shaft, but only the so-called apparent electric power. The real mechanical power is much less then. See here for details.
Also when milling wood, it is important to have high torque at high speed (up to 24,000 rpm). Unlike metals, wood has a poor thermal conductivity so tends to get hot, and when milling wood, the heat is evacuated nearly exclusively with the chips. Have you already seen this video? Look at the rotational speeds, they mill everything with high speeds.
For the difference between router and spindle see here.
Welcome to the forum!