Playing with a powerful cue action brings even the best cue actions into doubt. It could be a number of reasons.
Try the shot at different speeds of stroke, and number them 1-10. Start with 1, which should be just enough to pocket the ball. Then 2, a little harder. All the way through to 10 which should be as hard as you can hit it whilst staying in control of the shot. Notice at what number you start to hit the wrong part of the pocket you want. If it's at 7, this is normal as you start to lose accuracy around this speed. Playing at 7 or higher means the slightest bit of unintentional side, a little body movement and the cue balls reaction is magnified.
I've done this my self in the past when a shot caused me issues. I make a chalk mark 6 inches in front of the cue ball along the shot line and see how my cues tip is in relation to it after the shot. If it's over the chalk mark the shot is a success. It means I've cued through the white along the desired line. If I end up over the chalk mark but missed the shot, or hit a different part of the pocket it means I've either aligned wrong and cued across the ball, or I've hit it with a little bit of side spin because I wasn't aimed through centre cue ball.
Progression exercises like I've mentioned going through 1-10 can help you overcome playing with power. It points out your weaknesses at certain speeds, so when you miss you go back 2 steps and start from there. Eventually you become used to hitting these shots and you notice how shots should feel when they're successfull at slower speed, what muscles get involved and so on then you can try replicate it but just hit slightly harder.
A video would be ideal to see exactly what is going on so you can get more tailored help.