Your Red slime alge (Cyano) are basically the same thing. It is caused by silicate in your water. If the tank is fairly new. It is just part of the maturing process. But there are a few thing that you should do to get rid of this.
Most of the time this first outbreak in a new tank last about a month.
Yes the lights do not need to be on that long. 8 hrs is plenty. Someone mentioned RO/DI water. Are you useing this? or did you set the tank up useing just tap water. If that is the case, you need to start doing water changes useing RO/DI water. and keep up with them.
Your next corse of action is the flow. what type of flow do you have. The flow thru your tank should be 10 to 20 times the gal. so a 75 gal tank should have at least a 750 gal an hour turn over or more. That is why we use powerheads. If you don't already have some power heads in your tank get a couple at least two. and put them in the tank so the water everywhere is moved. You do not want any dead spots. Try to put one so the water is blown across the back of the tank, from one side to the other, and the other point it so it should blow against the front of the tank and bounce off at an angle. That should help with the flow.
Now I noticed you saiid you are a day care provider, and the kids love to watch the fish. Does this also mean they fight to feed the fish also. Maybe the fish are getting to much food. and thus to much waste. Not eating food. and the potty the fish are making. make sure you have a super good filter system going on that tank. and do weekly water changes. That will help with the extra nitrates and the red slime.
So check your lights, flow, water (ro/di), filtration, and water changes once a week. It should take care of itself in a few weeks.
By the way testing your water for phosphates wont show silicates. there is a separate test for that. and silicates is what causes Red Slime. You get silicates in your water mainly from either useing tap water or play sand intended for the play ground not a saltwater tank. You didn't by chance want to save $$ and use play sand like for the play area at the daycare. That sand is much cheaper than the sand at the LFS. If you did, let us know. We are playing in a whole different ballgame then. and you have some work to do.
Do not waste your money on treatments. They do not work. I know of what I am speaking. I know so much about Red Slime, Because I battled it for over a year. I bought my water at a LFS. that really all they wanted was to make $$. So they never changed their RO filters. I paid $1.25 a gal. for water that was worse than tap. And every week I paid $25plus dollars for Red Slime treatment. It would work for a couple days, and come right back. It took me months of reading and looking for answers. That is why I know. You can treat all you want, but if the root cause is still in there, It will come right back.