Tradin,
The double set trigger (DST) on your rifle is badly out of adjustment and is currently dangerous. This is the result of someone turning the little screw between the triggers, without understanding what he was doing. When you pull the rear trigger, until it "clicks", the front trigger should hold it in that position. BTW, verify the rifle is completely unloaded while checking, adjusting it. The rear trigger is actually a "striker" that strikes the "kick off" that is connected to the rifle's sear, causing it to fire. The adjustment screw adjusts the engagement of the sear between the two triggers. The "fix", hopefully, is to turn the adjustment screw until it holds the rear trigger (even when bumping the butt on the floor or with your hand). If it can't be adjusted to "hold", the problem might be one of two things. The little sear between the triggers may be damaged so it won't hold, or the small sear spring may be weak/broken/or missing, leaving the sear unable to hold. To fix this will likely require the services of a gunsmith, such as "Dutchman Wood Works" or "New England Custom Guns". Fortunately, unless something else needs attention, it may only be necessary to send the triggerguard assembly with the DST attached. The gunsmith should be questioned about this. With a properly adjusted DST, you should be able to "set" the rear trigger when you put the rifle to your shoulder and touching the front trigger should fire it, when you are ready. It shouldn't fire without your deliberate action, if properly adjusted and in good working order. Don't let this make you abandon DSTs, they are wonderful devices. Good luck.
Mike