Crossloop Connect is so much easier than trying to deal with Remote Desktop. Install it on both machines, initiate the session on the host, your parents machine. Connect using the code on yours. They click Yes and you are on their PC.
Sounds like CrossLoop Pro should be everything and more for your needs. It's $69 yearly, and it meets all your requirements from what I could see.
Just try using http://www.crossloop.com instead, lots of professionals that can offer you that service, also you watch them work so you learn :)
Also you can start to use crossloop to sell your services as well.
I use it for tonnes of people (I actually use it for business) and it warns me that it suspects commercial use but I can still use it...
I would like to actually pay for it but there isn't any decent pricing option for a small/freelance business. Farrrr too expensive for me - that http://www.crossloop.com looks good though, and a decent price.
Personally, I use "CrossLoop" for the simple-minded fellows who own PCs and need Technical Support. I never leave a clients computer without install CrossLoop on it.
The only time this simple-to-use VNC software won't work is..of course..when your clients don't actually have an active connection to the internetz.
Edit: I use CrossLoop over other VNC programs for two reasons. 1: It's simple to figure out for a n00b. 2: You don't need to worry about forwarding ports.
Computers/tech. Ok more specifically computer troubleshooting, servers, programming. For those techys out there - you can make a decent amount setting up people's sites using a CMS - the problem is finding those with the deep pockets who are looking. I used rentacoder-vworker-now freelancer to find some work in the past - but the pay sucks. Find the right person and if you install a CMS - they will shit bricks on how awesome you were to put together that site.
I'm also pretty good at warranty-voiding things like rooting - I'm not talking about the process of (it's pretty simple - just follow directions) but what to do if stuff doesn't work. And the related things that you can do with root.
I have used stuff like crossloops in the past - and they have ways of getting paid but I would rather do something constructive than sitting around all day waiting to help something. Here is my profile.
Perhaps we should add a feature like this to a subbreddit (/r/computerhelp )? Like a list of people who you can contact for free and/or paid support (along with some sort of vetting/tracking system)?
Hmm I am good at finding things on the internet. I won't expand on things, but use your imagination and I can probably find it. I have thought about something like chacha - but I don't think that pays very well.