I am not going to take sides. I am just going to say this, yes you should cycle. The microbe lift idea given by Daniel is a good one and I hope that you do get some sort of bacteria that is comparable to it (don't think you can get microbe lift there?) because it really will help your pond. You do need to do a 10% water change once a week (contrary to popular belief) because a man made pond is not a natural body of water.
In order to keep your pond healthy these are the things you need to do;
1. You really should cycle it, and put fish in slowly, two at a time.
2. Buy Microbe lift or something comparable. You'll put this stuff in once a week and it does keep a good balance in your pond.
3. 10% water change once a week, without any fresh water coming in (like a natural pond) you have to take some out and replace with fresh. What is happening in your pond is the minerals are being leached out by fish and plants. You will put these minerals back in the pond when you put in fresh water. These minerals are needed to keep your fish and pond healthy, I do believe that you could have a pH crash if the minerals are totally leached out (I could be wrong I don't have my books here for reference).
4. Water chemistry test kit. Very important, you need to know the Ph, Nitrite level, and ammonia level in your pond. Especially now since you have a new system. Your nitrites are going to be going all overt the place. Without knowing what is going on in the system you could get into trouble. I would put 3% salt in the pond just to be safe.
5. When you clean your filter clean it with pond water, just clean it so it's not clogging up, you don't want to knock off good bacteria.
There are some other things that I can think of, but not sure if they are as important.
I am sure that you may have eventually had an accident with the lily pot spilling over, I've done it several times in my pond and it makes me angry! Of course I can only be mad at myself.
Daniel is right though you should try and get along with your parents on this project. Your parents may not be totally right but that is because they haven't been educated on how to care for a pond. You need to educate them so that they understand. Once they become educated then you can be mad at them when they do it wrong

. I hate to see you get upset over something that really is a lot of fun. Send your parents here, or there are other websites such as koivet.com that has a lot of info. koicarp.com is a very good site that is from England. They just need to be taught on how to care for the pond.
Goodluck! Remember this is the best hobby one can have and being able to share it with others makes it all the more enjoyable. Educate your family.
Scott