Parents, Grandparents hugging and kissing adult children and grandchildren of the opposite gender:
Kissing and hugging is permitted between parents and children even if they are of the opposite gender [and even if the children are now adults]. Thus, a mother may hug and kiss her son [of any age] and a father may hug and kiss his daughter [of any age]. [See Q&A regarding if she is married!] Kissing and hugging is likewise permitted between grandparents and grandchildren of the opposite gender.
May a parent/grandparent hug a married daughter/granddaughter?
Some Poskim rule it is permitted for a father or grandfather to hug and kiss his daughter/granddaughter even if she is married. Other Poskim however rule it is forbidden for them to kiss or hug a married daughter/granddaughter. Practically, it is permitted to do so, although one who desires to be stringent upon himself is blessed.
Relatives showing affection in public:
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. On the other hand, one can argue that affectionate touch between such close relatives does not lead others to any immoral thoughts. 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. However for a parent/grandparent to hug their young child in public is certainly permitted.]
 Michaber Even Haezer 21:7; Kiddushin 80b; Kitzur SHU”A 159:10
 Perisha 21:7; Beis Shmuel 21:15; Beir Heiytiv 21:15; Taharas Yisrael 21:17; Chochmas Adam 125:6
The daughter/granddaughter/mother/grandmother is a Nida: The above allowance applies even if the relation is a Nidah. [Betzeil Hachochmah 3:12]
 Chelkas Mechokek 21:10 based on Kiddushin 81b; Beis Shmuel 21:14 [see there for a long discussion on this topic]; Pischeiy Teshuvah 21:5; Igros Moshe Y.D. 2:137
 Beis Shmuel 21:14 that when both are clothed there is no prohibition to sleep together even if she is an adult and is married; Pnei Moshe 21:5; Beir Heiytiv 21:14; Aruch Hashulchan 21:10; Taharas Yisrael 21:17; Nidchei Yisrael 24; Divrei Yatziv Even Haezer 36; Chochmas Adam 125:6 concludes with a Tzaruch Iyun; Betzeil Hachochmah 3:12
 Mishneh Lamelch on Rambam 21:6-7; Nesivos Shabbos 13a; Meiri Kiddushin 81b; See Betzeil Hachochmah ibid
 Betzeil Hachochmah 3:12 as rule majority of Poskim ibid
 Betzeil Hachochmah ibid; Beir Moshe 4:145; Igros Moshe Even Haezer 1:60 and 4:63; See also Od Yosef Chaiy Shoftim 21 that a Baal Nefesh is to be stringent to himself. [does not specifically stipulate regarding daughter that is married].
 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.
 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.
 So is implied from the ruling of the Taz and Beis Shmuel ibid that there is no Zichron Tashmish by such relatives
 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.
 Pashut, as people do not view this erotically.