Did Your Twins Love Each Other as Toddlers?

What I mean is, did they love each other so much they pushed one another, or pinched one another or bit one another and though this was a good thing?

Twin "A" is the instigator in all things pertaining to Twin "B" and fighting. I think she thinks this is a good thing and wants to see how far she can go before Mommy tells her to stop hurting her sister or Mommy will send her to her room.

Twin "A" does not like time out or being told NO. She also is not a fan of me disciplining her. But if I do not, then she will think what she is doing to her sister is acceptable and that if she can do this to her sister, she can do this to others.

So, what I am thinking is, does this mean Twin "A" loves her sister and this is the way she shows it? Gosh, I hope not and I hope she will grow out of this stage soon.