My son used a pacifier quite a bit from birth to 4 months. Then from 4 months to 6 months, the rule was he could have it at naptime and bedtime, or "emergency" situations like a long car ride or church. At 6 months, the pacifier was gone for good. He fussed the first couple of nights, and then he was done.
My point is, newborns have a NEED to suck to calm themselves, whether it's the breast or a pacifier or their hands. I wouldn't worry about her being hooked at 2 months.
My pet peeve is seeing a toddler walking around with a pacifier, but don't feel like you are on some sort of slipper slope and you'll be bargaining with her when she's 3 to give it up. I read that until a baby is in the 4-6 month range, the only way they can calm themselves is by sucking, and I found that to be true for my son.
Also, I don't think your daughter is old enough to "get" why you are moving her hands away when she tries to suck. If this was my kid, I'd let her suck on her hands if she doesn't want the pacifier. I think thumb sucking is a whole other deal--I mean, unless you tie her hands behind her back, she's going to suck on her thumbs as long as she'd like--they're attached to her.