First batch of cider with my daughter

[Vic]

My daughter wanted to try to brew some cranberry cider. We started with three gallons of organic apple juice, the blow off tube is gurgling and everything looks good so far.

My questions:

Is it best to add concentrate flavoring or actual juice in the secondary? And if I have head space in my secondary fermenter, should I fill it up with more juice to avoid oxidation?

She wants it sweet and sparkling both of course. What's the best way to achieve that?

[squeegeethree]

Add either but understand the more juice you are adding the more diluted and lower in ABV it will likely become. Reducing headspace is always a good idea IMO as long as you can avoid blow off.
If this is your first batch then honestly you should settle for dry and sparkling. Concentrate on getting the sparkling process down before attempting a sweet cider. To get it sweet you need to add lactose, or back-sweeten and pasteurize. Both involve a level of care and understanding that I would try on a later batch.
Look at the carbonation calculator now to figure out what will be expected of you in the future. Remember your gravity must be stable for a minimum of 3 days before you take on the bottling process

https://www.northernbrewer.com/pages/priming-sugar-calculator

[camelotmt]

I am pretty new to brewing myself, but I also like a sweet and sparkling cider and I was able to successfully do that in my first brewing attempt by back sweetening and then bottling and pasteurizing. I followed the process from this blog: http://www.brewunited.com/index.php?blogid=80

I prefer to sweeten with honey because I'm not a fan of processed sugar, but you do need to make sure that the honey is distributed evenly so that the bottles will ferment evenly. I really like the plastic bottle trick (make sure it has about the same profile as your bottles) to know when there has been enough fermentation for your cider to be sparkling. My first time, it took about 3 days. This year, it was much closer to 24 hours (I didn't use gelatin this year, which may have been the difference). Both times I back sweetened to about 1.050, which I found palatable once it dried a bit during the secondary fermentation.

[brewdvm]

Reducing head space is always a good idea. It's difficult to make a sweet and sparkling cider without a kegging system, but it can be done. I would recommend a slow and cold fermentation if you can achieve it. 55 to 60 degrees for most of the cider yeasts out there. You'll avoid the higher fusil alcohols that will give you headaches and taste like gasoline. I don't worry about racking to secondary at this temperature. Give it a good 3 to 4 months. Then add your cranberry juice, bottle it, and then pasteurize the bottles when they reach proper carbonation. I've used a plastic soda / pop bottles as a gauge for carbonation level. When it gets firm, you're ready to pasteurize. This step can be dangerous as bottles can crack and expode, so warm the bottles up gradually. Also, do it in a cooler filled with hot water and close the lid to reduce damage of flying glass. 165 degrees for 20 to 30 minutes should be enough to kill the remaining yeast and prevent further fermentation. You could add your cranberry juice earlier, ferment that out and then add frozen apple juice concentrate at bottling. I've done cranberries before. I think you'll like it. A lot of flavor remains unlike some of the other fruit options. If you have a kegging system, add your juice to the keg, put it on some gas in the fridge, and you'll have very little additional fermentation at this temperature leaving the cider sweet and sparkling. Good luck.