So, let me paraphrase back what I am hearing: You want to disconnect your grey water from the common dump valve, (I assume) add a second dump valve for the grey water only, which, when dumping, would drain through a filter system and then onto the ground. You want to attach the black tank dump valve directly to a tote and leave the valve open all the time so that black water never stores up in the tank, but goes immediately into the tote.
If the above is all correct, I would offer the following: You should be able to accomplish what you want to do without disturbing your existing plumbing, assuming that original common dump valve has a valve for the black tank and one for the grey. You really don't want to leave that black tank valve open all the time--you want some fluid in the bottom of the tank, and to let it fill up until it is ready to dump all in one go. If you leave the valve open all the time, you will very likely get an accumulation of solid material in your black tank.
Similarly, you would want to let your grey water tank fill up. You could then use the grey water as a flush of the hose going to the tote to help clean rinse away the black water. You could occasionally attach the hose comeing from the dump valve to your sand filter and dump the grey water as needed. If you don't want to hassle with moving the connection around, and you want the grey water to drain continuously, then you will have to separate the dump valves.