How to Expiate for Intercourse during `Umrah
Question

I live in Saudi and my wife came from outside Saudi. We met in Jeddah when we were in Ihram for `Umrah only, and we went to Makkah. In the hotel intercourse took place before `Umrah, then we went to At-Tan`im and entered Ihram, and we did a new `Umrah. What is the ruling?
Praise be to Allah.It is not permissible for one who is in Ihram for Hajj or `Umrah to have intercourse until he or she has exited Ihram. If a person has intercourse during `Umrah , before completing Sa`i, the `Umrah is invalidated, but he has to carry on and complete it, then make it up by entering Ihram from the place he entered it the first time, as well as sacrificing a sheep on behalf of each of you, to be slaughtered in Makkah and its meat distributed to the poor (of Makkah). 
With regard to intercourse after Sa`i and before shaving the head or cutting the hair, it does not invalidate `Umrah, but Fidyah (ransom or expiation) is due for that, with a choice (between offering a sacrifice, fasting for three days or feeding six poor persons). 
Your going to At-Tan`eem was of no use, because you are still in a state of Ihram for `Umrah -- even if it was spoiled -- so it is not correct to enter another Ihram until you are done with the first one. 
Based on that, what you did of the actions of `Umrah is regarded as the completion of the spoiled `Umrah, and you have to make it up. You should enter Ihram from the Miqat where you entered Ihram the first time, and slaughter a sheep on behalf of each one of you. 
Shaykh Ibn Baz (may Allah have mercy on him) said: 
“If you have intercourse with your wife, it invalidates your `Umrah, but you have to complete it, then make it up again from the place where you entered Ihram the first time. Additionally, you have to offer a sacrifice, which is a one-year-old sheep or a two-year-old goat, to be slaughtered in Makkah and given to the poor there. One seventh of a camel or a cow is also acceptable." (Fatawa Islamiyyah). 
Some scholars are of the view that what is required of one who has intercourse during `Umrah is to offer Fidyah, with a choice between offering a sacrifice, fasting for three days or feeding six poor persons, whether he had intercourse before Sa`i or after, as it says in Sharh Muntaha Al-Iradat (1/556). 
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: 
“`Umrah in which intercourse takes place is an invalid `Umrah and you have to sacrifice a sheep, to be slaughtered in Makkah and the meat distributed to the poor; or feed six poor persons, giving each one half a Sa` of food; or fast for three days. You also have to do another `Umrah to make up for the one that was spoiled."(Al-Liqa’ Ash-Shahri, 9/54) 
To sum up, you have to do three things: 

Repent to Allah, may He be Exalted, for doing something that was forbidden while in Ihram and spoiling the rituals which Allah commanded must be completed.
Do `Umrah again to make up for the spoiled `Umrah; you have to enter Ihram from the same Miqat as you entered Ihram for the `Umrah that was spoiled.
Offer a Fidyah (ransom); each of you (you and your wife) has the option of your choice: either sacrificing a sheep , or fasting three days, or feeding six poor people among the poor of Makkah. If each of you sacrifices a sheep, that is preferable and is more on the safe side.

And Allah knows best.