Yes, I would cut off branch B and leave A as the modified central leader. Like a hair cut it will grow back. I would leave one bud, and not cut it completely off. Always leave the collar when removing all of branch, so it can heal correctly. I think you should leave one bud node, and not to the collar, as a branch might grow in a better direction from that bud. You can always cut it off again. In general, you should trim all last year's growth by 1/3. Even up to 50% if you want a small tree. yes, you are cutting off fruiting wood, but we want to establish the tree first, the structure, and the roots, worry about fruit later. In the long run the tree will produce better doing this. You want 3 or 4 main scaffold branches. nice if not exactly across from one another but spindling up. Trim these lateral scaffold branches to create secondary branches on them that will be where the fruit will be produced once larger. If you are looking from above the plant you want your scaffold branches to be say at 12 O'clock, 3 O'clock, 6 O'clock, and 9 O'clock. (this is ideal, hardly ever happens that well!). Hopefully these will be spiraling up the central leader, and not directly across, but that is OK. If a branch on the central leader is directly above another branch the top branch will shade the bottom. Remove the top one. The top grows more aggressively, once lower wood is gone, it's gone! So I always leave the lower branch. Always try to prune just above an outward facing bud, and on a slant (top of slant closest to bud), leave a little stem above the bud, 1/4 inch or so. Not directly above the bud. You did well removing crossing branches and ones going inward, but I would trim all branches on a young tree about 1/3 of last year's growth should be removed. I myself want small trees so I remove 50%, sometimes more, and almost all of it once it reaches the height I want. I'm growing mine with an open center. Like a bowl. Also remove secondary branches on the scaffold branches that are growing straight up, or straight down. You want them growing parallel to the ground, or close! Hopefully others will respond too, I'm not like super experienced, but I think what I'm saying is correct.

Hi JyLu, Take a look at this thread where I posted some pictures of a peach tree that I pruned just a few months ago. I headed it off and only left one scaffold which has fruit on it. All the other scaffolds you see were only buds when I pruned this tree roughly 6-8 weeks before I took the picture. Next year those new scaffolds will be producing fruit. The tree was not even dormant when I pruned it. Here is a link that might be useful: Should I prune this bareroot peach?

You can't really do that with peach trees as it may kill it. Only new wood can be counted on to generate new buds next year. The tree was trained to be an open center from close to the ground. If you have squirrels or coons (and no adequate chase dog) and don't plan an electric fence you may want to tape up a branch to grow vertical so you can start your scaffolds at about 4'. This will allow you to attach something to the trunk which will prevent these animals from getting up the tree.

That looks like a pretty extensive mulched area- really pumps up the vigor. How come you didn't fruit them this year, they certainly look like they were big enough. If they did bear good crops than you definitely need to think about how to ratchet down that growth. One way is several prunings during summer, although when trees are in fruit you have to be careful not to prune too much to where you cut down on sweetness of fruit. You should certainly prune all your most vigorous uprights ASAP as well as 2-year wood higher in the tree than you want fruit. I don't think you have to worry about when you prune there and I'm confident it's OK now.