Minimal amount of products/water/conditioner should be used in detangling. the lady above who mentioned alcohol, that is a good idea to use on your fingers, and i would suggest putting a little alcohol water on the comb after detangling with the fingers.
then you could put your hair in plats after detangling before you clarify and deep conditon. i would dilute the clarifyer with water big time or use diluted acv as not to tangle your hair back up, and wash each plait separately.
then you can deep condition and detangle again with the conditioner. i remember taking out braids as a kid, and i would comb them out then wash them, but since you have that weave thing i think its a bad idea to use a comb without at least using your fingers first.