First step is too ease up on those caps.
Second step:
On your ValPlayer object in the 8-Direction settings, untick the use default controls option.
Then you can make the events for your movement control and add any conditions into them. Something like:
On 'left arrow' is down
&
Animation "punch1" is not playing
&
Animation "punch2" is not playing - 'ValPlayer' Simulate control left
On 'right arrow' is down
&
Animation "punch1" is not playing
&
Animation "punch2" is not playing - 'ValPlayer' Simulate control right