Moving two servos in opposite directions using the Servo library is not a problem. Moving two servos in opposite directions using the VarSpeedServo library is.
You can emulate what VarSpeedServo is doing by using small intervals between small steps.
if (buttonPushCounter % 2 == 0) {
myservo.slowmove(0, 180);
} else {
myservo.slowmove(180, 180);
}
I fail to see how the else block is accomplishing anything. Generally, when you struggle to figure out what to put in the else block, it's a sure sign that no else block is needed.
And, of course, what AWOL said.