D.,
No one, not even a relative, has the right to hit your child. Did you make it plain to her when you were talking about this problem that you didn't approve of her method of switching? If you want her in your daughters life you will have to make it plain to her that if she watches your child, it will be with your method of punishment, not hers. I definitely don't beleive in switching. I grew up with that only I was able to run away from my mother. However, instead of the switch since she couldn't reach us, she used a broom because it had a longer reach.
You need to sit this realative down and talk to her about your treatment of your daughter. Please do not take offense at this but it sounds like she might be a little overbearing. You will have to stand up to her. You will find the strength. It is for your daughters good, and yours.
My suggestion on getting your daughter to stop biting is when she does this, you have to take hold of her hand and chin and make it clear to her that biting is wrong. Say no very strongly, shake your head and make a biting motion with your mouth and teeth. Make sure that you use your firm voice and a firm look to your eyes. My daughter is 7, when she does something wrong now, all I have to do is stare her down. I went through the biting, hitting, tantrums etc. Now when she acts up I just call her name in a very firm voice and give her the 'look'. My step daugthers, even though they are in their 30's, are still afraid of what they call the evil look. It is effective, I do not have to hit and I rarely have to repeat myself. In fact I have 5 grandchildren that know that look also. My step daughters also learned that look.
I wish you luck with your relative, make sure she understands that you don't approve of her methods.
E.