Audio gain for subclip in Premiere Pro
I'm not sure why you would want to use normalize at all. You should use audio tracks and place the audio you need to adjust on it's own track. 

Then, using the audio mixer, apply dynamics to the audio tracks. You can then use the compressor within the dynamics filter, which you can use on all your tracks, to get your dynamic range all in line. 

On the clip that needs to be (from what it sounds) adjusted up, in the dynamics filter for that track/clip, you can from there manually adjust the gain up- it's a pot/knob center column bottom. Use a ratio of about 2:1 to 4:1. 

Last, click the checkbox on the bottom right of the dynamics filter for each track to enable the limiter. The limiter; a good setting is -2 db. 

This will balance out your audio so the soft sounds are adjusted up and can be heard, and the loud sections are not adjusted up; resulting in overmodulation. Its a much better way to smooth out your audio, decrease the dynamic range, and end up with audio that sounds far more balance. 

Once you learn how to effectively use the dynamics filter on tracks, I think you will find you will never, ever, use the Normalize filter again.