I have used this method to remove gum from my sons pants when he sat on some at a football game and it works very well. I used white vinegar, but I think either kind would work.
Pour some vinegar into a cup or shallow bowl and put the part of the clothing with the gum on it into the vinegar and let it soak a half hour or more, then put it in the washer with the vinegar still on the gum and wash as usual. The clothing will come out of the washer with the gum completely gone from it. It is the best way I have ever tried on gum in clothing.
Love in Light and Peace,
Winds of Change