First of all, please don't douche.. douching only upsets the natural flora in your vagina and you will open yourself up to all kinds of problems with yeast infections
. If you want to try anything at all like that, use coolish water.
This can be an issue with men with thinner (less wide) penises during intercourse, especially circumcised men (who don't have foreskins to provide extra friction), and it's common enough for it to only become an issue once the female partner is more easily aroused and comfortable -- which is as it should be -- because arousal and relaxation cause that extra lubrication and a less tight vaginal canal and opening..
You really don't want to have a "drier" vagina, because you're supposed to be aroused and wet with genital sex, and sex with a drier vagina can irritate your tissues, as well as just not feeling so good. There's also no sound way to bring about a "drier" vagina. Eventually a too wet vagina, will become just right over time.