Agree, its algae. I assume you've been turning the light on so the kids can see the tank but are you leaving it on all day?
You are now past the nitrite spike and thus entering the 3rd phase of fishless cycling. Several things change now. If you've been reducing your ammonia concentration during the nitrite spike, its time to ease it back up to 4-5ppm so that you can get as close as possible to 5ppm for the finish. The other thing that changes is that all that ammonia getting put in day after day is being cycled through to create nitrate(NO3) and its now gone so high (past 160ppm) that the nitrate test is probably beginning to get even more wacky. To me, this means its now a good time to consider beginning your practice cleaning sessions for becoming a fishkeeper. Occasionally (I would say every other weekend or every weekend or something but you may be home some with Lily Rose and have a very different than normal schedule) when its convenient I would do a big gravel-clean-water-change (not a filter clean) and then be careful to refill with conditioned, roughly temperature matched return water and recharge your ammonia back up to 4-5ppm and recharge your baking soda if you're using that. I'd make the water change right down to the gravel. What this will do is get most of the nitrate(NO3) out and make sure that its not slowing the N-Bac development. It will also refresh the calcium and iron and other trace elements, while getting rid of algae spores and other things. Your testing will now move up to every 12 hours if its not already there but of course nitrate(NO3) does not need to be tested for all that often and pH need not be every time, especially if you're using baking soda.
The goal now is to watch the N-Bacs be able to clear the nitrite faster and faster, starting by getting it to zero ppm within 24 hours after NH3 was added and then working down to 12 hours after it was added. Ammonia of course is already there but don't be surprised if it seems to lose ground at some point as it frequently does seem to do this.
~~waterdrop~~