Hi K.,
I also have a 2 1/2 yr old daughter. I pierced her ears in mid April. I bought 14k gold earrings in a kit, along with an ear care antiseptic. I started using a dropper to put the antiseptic on front/back of my daughters ears. She too got upset, and didn't want me to touch her ears. Even though the piercing process was quick (the gun method), it still upset her.
I did the dropper/antiseptic twice a day (morning & evening) for 2 wks, then did it in the evenings just before bedtime.
She too did not like me turning the earrings. At first, I didn't think of doing this until I had heard someone say that the flesh of her daughters' earring grew around the back post. I now turn her earrings occasionally, and she still says "no touch".
I'd use the dropper to apply the antiseptic, and maybe warm up the antiseptic in warm water. Maybe during your daughters bath, she will find in less noticable.
Best of luck!
Judy