Newer brewer looking for input on process

Hi, I am new to home brewing, thought Id try my hand at a old school fermented ginger beer. Im about halfway through the process and was looking for some tips or guidance on how I plan to proceed.

So far, I made my ginger bug (like a scoby for kombucha, or starter for bread) earlier last week, and this Saturday I boiled ginger, spices, lemon juice and common white sugar with purified water, let cool to about 90F, and then mixed in my bug. My hydrometer showed 12% potential ABV (@60F). I have batch now fermenting to two glass 1gal jars with screw tops and air locks.

Going forward I want to bottle half as is, and boil the other half to remove alcohol so my pregnant wife and nephews can enjoy. Obviously I will have to inject CO2 in the non alchohol batch, but I would like to bottle ferment the normal batch to create natural carbonation.
I also want the finished product to be fairly sweet, not like soda mind you, but more like a dessert wine, so I was planning on dosing with sugar again before bottling to get the right balance.
What I am fuzzy on is how to dose the normal batch in a way that it recarbonates without blowing up or converting all the sugar into more alcohol, and retains the sweetness.
Thanks in advance

Backsweetening with anything that yeast eat before bottling will be a problem. The yeast will consume that sugar and over carb your Ginger Beer. It also would not be sweet afterwards.

Could you backsweeten with an artificial sweetener? Erythritol? Stevia?

If you want the alcoholic batch to be fairly sweet, your best bet may be to stabilize (with sulfite / sorbate) and force carb it, too.

Controlling residual sweetness with bottle conditioning is going to be challenging.