Control of your carbonation level is a matter of taste and safety. You can control the level of carbonation by using a precise amount of priming sugar. This is not impossible with fruit juice but it would require some serious measurements of the sugar content of the fruit juice and calculating the dose for your batch of cider. In general, 4.2 g/l priming sugar will yield 1 volume of CO2 plus whatever CO2 is in solution (~1 vol). If you overdo it and you are bottling in beer bottles, they will burst under the pressure (bottle bombs). If you bottle in champagne bottles that weigh more than 800 grams, the bottles are less likely to burst before the crown caps start to leak.
Adding fruit juice or fermentable sugar to a non-sterile cider will result in renewed fermentation in the bottle that will almost certainly go to dryness leaving you with a dry carbonated cider. You can arrest this process by pasteurizing the cider in the bottles while there is still some residual sugar. This has its own risks due to bottle failure during pasteurization if the carbonation is high enough. Heating a pressurized bottle will increase its pressure. You don't want a bottle to explode on your kitchen stove. There are numerous posts on this forum by people who routinely produce sweet, carbonated cider that they pasteurize. There is also the option to bottle condition with priming sugar plus a non-fermentable sugar or sweetener. Lots of posts on this technique as well.
I seriously doubt it is possible to naturally carbonate cider in 3 days. The speed of carbonation in the bottle is a function of temperature, live yeast count, available sugar, available yeast nutrients, and added inhibitors like sulfite. In general, bottle conditioning takes several weeks. Mine generally take 45 to 60 days to reach full carbonation at 70 deg F.
I just read Pappers_'s excellent post on stove top pasteurization at the top of the forum and see he gets his bottles carbonated in a week! Reading between the lines, he must have a good crop of viable yeast when he blends in 25% fresh juice. Working under the assumption that his batch has gone to dryness (FG=1.000) and he adds fresh juice with an OG=1.050 he is carbonating from a new gravity of 1.013. Lets say he likes the sweetness to be at a FG of 1.005, he would have a carbonation level of 2.5-3.0 volumes of CO2. Three volumes could be pushing the safety range for thin walled beer bottles so go for the thicker variety.
