Yeah, you can clean it yourself. I have done this many times with my dogs!
Go to the pet store and get a bottle of Nature's Miracle. How big a bottle depends on how big the pee stain is.
If you happen to have a wet/dry shop vacuum, that will make it easier.
Pour clean water [no soap] on the rug, then towel dry it or vacuum it up. Do this 2 or 3 times to get as much pee out as you can. Then pour Nature's miracle on it and let it air dry. Don't towel dry it or vacuum it up.
When this is done, look at it and smell it to see whether it is all the way clean. If not, you have to use the NM again, and more of it this time, because it is probably because it didn't soak in as far as the pee did.
Actually, you can do this with white vinegar, which is cheaper but more work. Instead of NM, pour white vinegar on the carpet, towel or vacuum it dry. You have to do this more times than you do with the NM. Leave the vinegar on the carpet 15 to 30 minutes at least, each time. And when you believe the stain is all gone, you have to dissolve some baking soda in water and soak it with that to get out the vinegar smell. It only takes a few minutes to neutralize the vinegar smell.
If the carpet is wool, make sure you dry it flat, so that it doesn't get mis-shapen as it dries.
Dogs will tend to pee where they have peed before, and any residual pee scent will make them even more likely to. They can smell it even when you can't; so it is important to get the scent all the way out.
BTW If the carpet is wool, steam cleaning will wreck it. It could also set the stain and make it permanent.
Also, this method will clean up your baby brother's pee stains just as well, when this becomes necessary! It cleans poop stains as well.
It sounds like your parents are under a lot of stress. Once you have mastered the art of cleaning up pee and poop, you can help with the baby too.