Lovebird Help???????

About 4 months ago, I got my first hand-tame lovebird. He is super sweet, and would never even offer to bite me. I would let him out of his cage for about 5 hours a day. School was making me busy, because I enrolled in the middle of the year, therefore it was occupying a lot of my time. So I had to shorten his outside time down to about 3 hours a day. I felt sorry for him, so I bought him a "playmate". She is also hand-tame, but when I let them both out of their cages, they peck at each other. I was told that this happens, and I need to let them get used to each other. My first lovebird is a little over 9 months old, and the female is a little over a year old so there isn't much age difference. Also, another problem is, when I let the new one out of her cage, she flies directly to my shoulder, but will peck at me when I put my fingers around her. I think she just needs to get used to me, but I don't know. One more thing, both of their wings aren't clipped, my mother wants to get a vet to clip them, but I think they should keep their flight feathers incase they start to fight so one can get away. Sorry for so much questions lol, but could someone help me out?