I stop feeling any concern toward you when you state you was planning on getting rid of another family pet over a pissing contest with your 19 years old son.
You would need to get very low not to have the moral high ground on you my friend hell you would need to dig a tunnel half way to China at least.
Second somehow if it matter greatly to you, you would find the 100 dollars or so to get the cat check out by a vet.
Your Cat may have a medical problem
Urinary Tract infections are a common cause of a cat peeing all over the house.
Often a cat will inappropriately urinate because of a medical condition. If you have problems with a cat not using his litter box please get him or her checked by a vet. Your vet can examine your cat for lower urinary tract diseases to rule out medical conditions which could be causing the inappropriate urination problem. For example a painful case of cystitis or urethral blockage may have your cat associating the pain of urination with it's litter tray and it will therefore avoid it's litter tray
Read these articles for more information
Pet Pee & Poop Problems - Discussion
Cystitis in Cats can cause inappropriate urination
Urinary Tract Infections in Cats
Diabetes in cats can cause increased urination and maybe your cat doesn't make it to the litter tray every time.
The Litter Box is dirty
Cats do not like using dirty litter boxes. Make sure you change the litter daily and wash the litter box with hot soapy water at least every few days. Scoop out soiled litter regularly in between.
Your cat may not like the brand of litter you have chosen
Maybe you have switched brands of litter or bought a completely different type of kitty litter. Cats are creatures of routine. If you wish to change the type of cat litter you are using then you can gradually introduce the new litter by mixing it with the old a small bit at a time until the new litter is accepted.
Often cats don't like the same nice smelling kitty litter that we might like. Avoid scented kitty litter.
The location of the litter box is not to your cats liking
Don't put the litter tray in a busy location or near a noisy washing machine for example. Put the litter tray in a quiet easy to access location and don't forget they like privacy too! Cats do not like to use the toilet near to where they eat. That's not surprising... neither do we! Move litter boxes away from feeding areas or where their water is placed. Do not put the litter box in a room or basement where the door may be closed and the cat cannot access it.
Your cat is spraying urine not urinating.
When cats spray urine it is not normal urination like when they need to go to the toilet. It is territorial and can be stress related.
Male Cat Spraying Problems?
The causes of spraying and how to prevent it
Your Cat may be stressed
Cats suffer from stress as well as humans. Cats are creatures of habit and thrive in a consistent and familiar atmosphere. When their 'comfort zone' is disrupted it can often result in stress which contributes to inappropriate elimination.
Read this article on Feline Stress Common causes, management and diagnosis of feline stress