Until what age may parents bathe their children of opposite gender, and may they shower together?
From the letter of the law, it is permitted for parents to bathe their children of opposite gender until the child reaches the age or signs of adulthood. The same applies regarding showering together, that so long as the child has not reached the age of adulthood, it is permitted. The age of adulthood is defined either by age [i.e. 11 years old for a girl], puberty [i.e. pubic hair], or maturity [i.e. the child reaches an age that he is ashamed to be unclothed in from of the parent]. When any of the above-mentioned signs of adulthood is present, it is forbidden for a parent to see his child of the opposite gender unclothed, and it is forbidden for the child to see his parent of the opposite gender unclothed. Furthermore, once a male child reaches this age, it is forbidden for him to see even his father unclothed.
Midas Chassidus regarding showering together: Many are accustomed as a Midas Chassidus and an extra act of piety and purity to abstain from allowing even small children of the opposite gender from seeing their parents unclothed from the time of birth. In fact, the Talmud states that it is for this reason that Hashem made the breasts of a woman by her chest, unlike an animal, in order so the child does not see her Beis Haerva. [Per the Rebbe’s directive of not seeing impure animals starting from birth, this would even more so apply regarding not seeing immodestly dressed men/women starting from birth.]
 This law is not mentioned explicitly in Poskim although is derived from the following other law mentioned: Prohibition to sleep together unclothed once the child reaches signs of adulthood. [Michaber Even Haezer 21/7; Michaber O.C. 73/3-4 and Admur 73/3 regarding Shema; See M”A 73/2 regarding seeming contradiction from Shema source; For possible answers of contradiction: See Perisha E.H. 21; Elya Raba 73/5, explained in previous footnotes] From the above source it can be understood that it is forbidden for a child to see his parent of opposite gender unclothed once he reaches the age/signs of adulthood.
 See previous Halachas where the age and signs of adulthood were discussed in length!
 See Rama E.H. 23/6 and Y.D. 242/16; Pesachim 51a
The reason: This is forbidden due to that it leads to forbidden thoughts. [Rama ibid] As one thinks of how he was born from his father. [Rashi Pesachim ibid]
 The reason: As everything a child sees, even from a young age, is encrypted in his mind, and hence it is proper to abstain them from seeing anything which can ignite their Yetzer Hara when they are older. [see Kav Hayashar 2; Hisvadyus 1984 20th Marchesvan 37 regarding impure animal]
 Brachos 10a; See Torah Leshma 215
 See Rebbe in Sicha ibid who references to Kav Hayashar ibid that one is not to look at impure animals being it becomes encrypted in one’s mind and will affect them when older. Thus, certainly one is to be careful in seeing immodest women, as it will affect them when older. The Rebbe at first states that one is to be careful in this matter beginning from age of Chinuch, and then states that one is to be careful even by a new born, and the Kav Yashar states that the primary cause of making one stumble in looking at women is not being careful in not seeing impure animals. Thus, certainly one should abstain even an infant from seeing immodest women.