Hmmm... we seem to have an Austin Powers fan here! I am pleased to see your daughter didn't name the CAE after the large red headed character from the last two Austin Powers movies!
The reason I asked about the water flow is that I have found when this is too low (usually from not cleaning the intake or the filter regularly) then the algae starts to become noticeable.
It looks like you are a doing 20% water change per week, which is fine.
Your lighting calculates out to approx 90 watts if they are T8s and you have them all on at once for 14 1/2 hours per day. I do not think this is an excessive amount of light, we have a 28w light going 24hrs a day over a 10 litre fry tank, which has Riccia and Stargrass in it, and it does not have an algae problem.
We have two foot tank that periodically gets both of the types of algae you have, when it gets too bad I trim the most algae covered plants and pull as much of the cotton wool stuff off as I can and then do a 30 - 40% water change for a couple of weeks, it seems to fix itself after a while.
We keep away from the chemical solutions, whilst they may kill the algae, they are not solving the problem of why you have it getting out of hand in the first place, it's like brushing away an annoying spiders web on your car wing mirror, but not removing the spider - next day the web is back again.
Even the snails aren't immune to alage!
Could you post a pic? Would be good to see what sort of plants and stuff you have in there.