Two years ago, I went to Hajj along with my wife and children. My son was six months old, and my daughter was four years old. I intended Hajj for them and performed the rituals for them. However, my infant son did not wear Ihram (ritual state of consecration) clothes, and my little daughter did not cover her hair during the rituals. We performed several ‘Umrahs in this way. My question is: Is it obligatory to offer a hady (Hajj sacrificial animal) for my son's Hajj and also one for each time of ‘Umrah as he did not wear the Ihram clothes? Shall I do the same for my daughter as she did not cover her hair during the rituals? Will they get a lesser reward? Is it permissible that the infant wears a diaper and underwear under the Ihram clothes so as not to catch a cold?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

You were required to avoid clothing your son in form-fitting items while he was in the state of Ihram for Hajj or ‘Umrah. Having done this anyway, if you were ignorant about the ruling, then you are not required to do anything. Allaah Almighty says (what means):

•   {And there is no blame upon you for that in which you have erred but [only for] what your hearts intended. And ever is Allaah Forgiving and Merciful.} [Quran 33: 5]

•   {Our Lord, do not impose blame upon us if we have forgotten or erred.} [Quran 2: 286]

In response to the supplication stated in the second verse, Allaah, The Almighty, said, "I will."

If you were aware of the Sharee'ah ruling, then you are required to offer a fidyah (ransom) from your own wealth. It is optional to fast three days, feed six needy persons (one half of a Saa‘ [3 liters] for each one), or slaughter a sheep. Slaughtering is not due in particular; but it is optional for you to do any of the above actions.

If your infant needed to wear form-fitting clothes to be protected from the cold, then you are blameless. But you are still required to offer a fidyah from your wealth, being his guardian, according to the preponderant opinion.

A separate fidyah is due for each Hajj or ‘Umrah where one of the restrictions of Ihram was not observed. A diaper is considered from the form-fitting clothes. It is permissible for the child to wear it, in case of necessity, but a fidyah is due as well.

On the other hand, you are not required to do anything for uncovering your daughter's hair during the rituals. 

Allaah Knows best.