I'm creating simple alphabet letters using normal household 2-part resin. It seems to be taking forever and a day to cure. I know things such as lamps and turning up the heating can accelerate curing time, but I wondered (because I saw it on a YouTube video, but no explanation), if I could use a UV light to speed up the curing time? Would it work? I'm helping my daughter but we're both completely new to this.
Short answer: UV light won't affect the cure of non-UV resin. Strong UV may even discolor or degrade some types of non-UV resin.
UV-curing resin works on a different mechanism. A one-part resin is stable until UV of a particular wavelength breaks down a component in the resin and causes it to cure. Any portion of the resin that doesn't receive a sufficient amount of that UV remains uncured. You need intense exposure to that wavelength, and it doesn't penetrate the resin well (so for thick castings, you need either extremely long exposure or building up and curing in thin layers).
Non-UV resin combines chemicals in separate resin and hardener to trigger a chemical reaction. Once the reaction has started, heat will accelerate it.
Some epoxy systems use a small amount of catalyst as the hardener to trigger the reaction. A catalyst doesn't react chemically. It's mere presence triggers the reaction. So you don't need much catalyst, and the exact proportion isn't too critical.
Other epoxy systems, like what you used, cure by reacting the resin and hardener with each other. They're generally designed to require equal amounts, or some other fixed ratio.
Non-UV resins generally harden in a matter of minutes to hours, although total curing for full strength may take up to days. If you mixed the epoxy and it's still sticky or soft after many hours, or say the next day, it will never cure. You may be able to harden or clean the surface, but there's no way to affect the resin on the inside.
Failure of two-part epoxy to properly harden is almost always caused by one of three problems:
Inaccurate ratio. Both the resin and hardener are syrupy, and that consistency changes only through reacting the two parts. If the ratio is inaccurate, the result will contain unreacted syrup of either the resin or hardener. That will be mixed throughout and will never harden.
Note that some epoxies are designed to be measured by volume and some by weight. Verify that you're basing your ratio on the correct type of measurement for the product you're using.
Inadequate mixing. Even if you start with an accurate ratio, if you don't thoroughly mix the two parts, you're left with a similar situation. There will be unreacted syrup of both the resin and hardener throughout the result. They will be isolated by the portion that does cure, and there's no way to get them to mix and react.
Old or deteriorated product. Most epoxy systems have a long shelf life. However, the components can eventually degrade through age or exposure to extreme temperatures. If you discover decade-old product that's been lost in your garage and decide to put it to use, it would be worth testing a small amount first to verify that it will properly cure.
There's also a fourth potential cause of curing problems that's not really the fault of the epoxy. People often experiment with mixing in various other things as colorants or appearance modifiers, thinners, or to change the physical properties of the cured resin. Some kinds of additives are incompatible with the epoxy or can interfere with the curing, especially if they're more than a small percentage of the mix.
Where to go from here
Stick your castings in a hot but not super-hot place for a day (not so hot that you can't comfortably touch it or that would damage the molds). Whatever is going to harden will harden. Then if they're still sticky, trash them and try again. If you're using re-usable molds, you may be able to clean them out, but don't reuse them if you can't get them thoroughly clean. Any unreacted resin or hardener left in the mold will create the same problem when you pour in properly mixed epoxy.