im sorry that you will have to go behind the familys back to get one ( testing kit) but beleive me ,and miss wiggle can back me on this one, i got my tank into such a dangerous mess when i wasnt testing ( not that i didnt have tests but i was wrongly making assumptions), its it vital that you test, its the first call, as an "illness" could quite easily turn outto be high ammonia, nitrite, and you would treat the fish to no avail, i can second the part about the livebearers, i have just got my very first female guppies, as i am now preapared for the off spring, i have bred platys and they breed at the drop of a hat, so you can be prepared for the numbers above++
its fair enough that you want a tank with little maintanence, and illness ( its what we all want) but effort has to be made to get it to this stage, regular water changes, excellent diet, compatible tank mates etc...
maybe you could introduce your family to this forum, let them have a read of problems that can happen and good that comes out of it ( tho best to show them the non emergency parts first), in just about evey post there will be a quote about water testing, and im sure you will go someway to sway them in your favour, im not sure how old you are, but if you are only young, then what about comprimising (sp) do some chores in turn for the testing kits and bits and bobs, as with everyting in life comprimise can be met, with maturity and paitenece

i wish you all the best i like the way you are thinking, very mature, but i feel a bit dis heatend that you would have to decieve your family , just for a test kit, parents can be really a pain sometimes lol, ask my sons and daughter

i wish you tonne sof luck with this and hope they come round to your way of thinking, it would make life so much easier for you
shelaghy xxxxxxxxxxxxxxxxxxx