Are you cycling the larger tank fishlessly or do you have another type of fish in there?
The nitrogen cycle can be a confusing thing, but it is something all aquarium owners should know about. I'll start at the beginning.
Waste excreted by fish is released as ammonia. Ammonia is very toxic to fish, and even the tiniest bit can kill or sicken them. I have a betta that almost died from .1% ammonia. He was badly stressed the week before though because he jumped out of water for 5 minutes during a water change. In a mature and cycled tank, there are lots of beneficial bacteria. That's a long word and it will be used often in my reply, so I'll refer to it as BB. There are two types of BB: 1) converts ammonia into nitrite, and 2) converts nitrite into nitrate. Nitrite is also very toxic to fish, and nitrate is only toxic in high numbers. If you have a planted aquarium, most of the nitrates will be sucked out of the water and used as plant food. If not, your fish rely on you to do waterchanges to keep nitrates under 20-30ppm. In a fully cycled tank, test results will always yeild ammonia: 0, nitrite:0, and nitrate: higher than the tap water. A cycling tank will show ammonia and/or nitrite like your tank does.
Now, tap water has very very little BB. There are not enough to make a safe and stable enviroment for fish, but there are enough to breed. Cycling a tank is pretty much breeding BB. Now how do you do it? Easy! Ammonia is "food" for the BB. Just like any other animal, if there is food, there is reproduction. They will keep reproducing until a balance is reached between "population" and waste production. The only problem is that this can take about 1.5 months and while your tank is cycling, water params will likely be high and your fish could suffer. This is why it is imperitive to closely moniter the water levels and do very frequent small water changes while cycling a tank. Its easier to start out with only one or two small fish than a tank's full capacity. Understand all that so far? Okay, now here are some shortcuts and pointers.
BB grows everywhere...the gravel, the ornaments, even the glass walls! BUT, the filter is the hugest colony of all. That is really the point of the filter: to colonize beneficial bacteria. What kind of filter do you have? Does it have a catridge or a sponge? Do you use bio-max or bio-balls? If you are not using either of those two things in your filter and you have even the slightest amount of space in your filter, I suggest you buy some. These will colonize huge amounts of BB and they will live there safetly. If you just have a cartridge or sponge and no room for those things, you must be very careful. Do not overstock your aquarium, and never ever replace or wash your cartridge. EVER! There is probably chlorine in your tap water, and by washing the gunk from the cartridge with this water, you are killing all of the BB and your cycle will crash. Replacing it with a new one will also crash your cycle. Even if the filter box says to replace the cartridge, do not do it because they do not care about your fish, only money. Cartridges will last a VERY long time, and you can safely wash them by swishing them in a bucket of dirty tankwater after a waterchange.
Do not use ammonia-chips/zeo-lite in your tank. This will disrupt the cycling process and they can be dangerous if they are not used properly.
Prime Waterconditioner is a miracle in a bottle. This stuff not only removes heavey metals and chlorine, but it also detoxifies ammonia and nitrite without disrupting the cycling process. This will come in handy a ton if you are cycling with fish, and its perfect for dosing the tank inbetween waterchanges.
Now, I think this shortcut will help you a bunch! The filter and media inside the filter on your smaller tank is most-likely loaded with BB. Hook that filter onto the bigger tank and move your fish to that tank as well. There may be a small bump of ammonia and/or nitrites, but other than that, this tank will be virtually cycled. It will be safe to remove the smaller filter in 2-3 weeks and your cycle will be complete.
For future refference, there are more humane ways to cycling than from scratch using a fish like you are trying to do right now. If the fish survive, they will probably be especially sensitive to poor water quality and illness, and may die an early death. If you do not have another filter to "seed" with, there are other options. One is Bio-spira. This is basically hibernating BB that can be bought to jump start the cycle and your fish will not be harmed. There are other brands, but this one has the highest success rate. Another idea is fishless cycling. In summary, you use an alternative form of ammonia to cycle the tank, adding no fish at all until the tank is ready. If anyone wants more info on fishless cycling, feel free to start a topic or send me a personal message. I think I've spoke enough already lol.
Got all that Vanessa? I know its a lot of info, but I broke it down as simple as I could. If you have any questions, please feel free to ask
Oh yah, gH and kH don't have to do with your cycle. kH stands for Carbonate Hardness, and this is what buffers and stabilizes your pH. A high kH is almost always a good thing. gH stands for General Hardness, and that means how hard or soft your water is. The prefference depends on the type of fish that you own. There are two ways of measuring kH and gH (like american inches and metric cm) and I don't know what yours are off the top of my head so I'll get back to you on those test results.