One of the toughest things in my open adoption has been the 'stranger danger' baby phase. For awhile all my birth daughter wanted was her mom and dad, and was very cautious around me. That was really hard on me, even though I knew I couldn't expect a baby to understand who I was. Eventually she warmed back up to me, but it was a tough phase. Offering her snacks was somewhat helpful too. How did you get through it?
It's probably small comfort, but a child's stranger anxiety phase is actually positive, especially in the case of an adopted child, because it shows that she is developing normally. Many children who have lost their birthparents and, possibly, other caregivers, before coming into adoptive families have a hard time learning to love and trust their adoptive parents and a hard time learning to understand permanence. As a result, they often parent-shop, giving hugs and acting charming around visitors, even very casual ones. because they think that these people may become their next Mom and Dad.
Many birthmothers feel that their birthchild "should" remember, on some level, that she spent nine months in their womb, feeling their heartbeat and, on some level, reacting to their every mood and action. You certainly remember your pregnancy with your birthchild, her little hiccups, her surprisingly vigorous kicks, and so on. But babies don't really have that much conscious memory of the prenatal period. What they remember is the same two faces they see as soon as they awaken and right before they fall asleep, every night. They learn to associate these two faces with good things, like gentle hugs, tender kisses, happy smiles, sweet lullabies, nourishment, and so on. And they learn to believe that those two people will always be there for them.
Luckily, the stranger anxiety lessens as a child grows, and is replaced by a more mature understanding of relationships. Yes, they can hug Grandma and their birthmother. But, no, they shouldn't hug the bus driver or the clerk in the store. Adoptive parents can foster a sense of connectedness between their child and the child's birthmother by encouraging visitation, if possible, by talking about her, showing pictures of her, explaining adoption in words that the child can understand, and so on.
One thing that people should understand is that, while a child is in the stranger anxiety phase, it is WRONG to insist on picking her up or giving her kisses. That will only scare and upset the child, and the child is quite likely to remember the behavior, and develop negative feelings about the aunt or grandfather or birthmother who does so.
Yes, adults can sometimes win the affection of a child by giving food treats, much as they do with pets. But that is a mixed blessing. Young children need to learn that they may take treats from others only if the parents say it's OK. Otherwise, they could eat something to which they are allergic, or which could be dangerous, such as a hard candy, which could choke a young child. Worse yet, treats can be used by pedophiles to lure children into harmful situations. While parents should cut grandparents and birthparents some slack, even these much-loved people should ask Mom or Dad before giving treats.
Be aware that, even long after the stranger anxiety phase ends, many children do not want to be kissed or hugged by people other than their parents, even if they are close relatives. This is particularly common among boys, though girls can have the same behaviors. They often see such interactions as "babyish", or they may not like particular relatives' scent or whiskers or whatever. Parents can often help these children learn other ways of expressing their feelings, such as by giving "high fives"or handshakes instead of huggy greetings. And the adults who would normally hug and kiss should not be offended or insist; they should come up with a greeting or goodbye ritual that works for the child and for them.