How can I keep homemade laundry detergent from disassociating?
You should use about 0.25 - 0.35% xanthan gum (thickening agent) per the total weight of the mixture. Using xanthan gum is kind of tricky. You want to thoroughly mix the gum with the baking soda and washing soda (maybe in a bag), and slowly add the sodas to the water while mixing. If you don't do this, the xanthan gum will form lumps that are difficult to manage.

Hydroxyethyl cellulose might also work as a thickener, but it could increase the sudsing effect. Also, I would try adding a dash of dish soap; only use about 1% of the total weight of the mixture though, or else the sudsing effect will cause the washing machine to foam over.