Relatives showing affection in public:[1]
It is permitted for a father/mother/grandfather/grandmother to engage in non-affectionate touch with their daughter/son/granddaughter/grandson even in public. [It is possible to learn in the Poskim that it is however forbidden for them to engage in affectionate touch in public, such as hugging and kissing.[2] On the other hand, one can argue that affectionate touch between such close relatives does not lead others to any immoral thoughts.[3] Practically, since in most situations it is not obvious to others that the two are father/daughter etc one is to be stringent, and so rule some Rabbanim of today.[4] However for a parent/grandparent to hug their young child in public is certainly permitted.[5]]
[1] See Beis Shmuel 21:12; Taz 21:1 that by the above relatives doing acts of non-affection acts in public [such as checking each other’s hair] does not arouse immoral thoughts being that everyone understands that they do not share an incestuous relationship.
[2] As the above Poskim only permitted these relatives to check lice in public, which is not an affectionate touch, while by an affectionate touch, such as hugging and kissing, certainly it can arouse immoral thoughts in the onlooker.
[3] So is implied from the ruling of the Taz and Beis Shmuel ibid that there is no Zichron Tashmish by such relatives
[4] So rules Hagaon HaRav Yaakov Yosef Zal, stating that those fathers who hug their older daughters in public are Amei Haretz and are causing others to stumble.
[5] Pashut, as people do not view this erotically.