My brother and I each have a house and on Eid in sha Allaah we want to slaughter one ram and give the other in charity without actually slaughtering it. Do we have to slaughter the two rams or not?.
What is prescribed in your case is for you to slaughter the two sacrifices. It is not acceptable for you to share in one sacrifice, because you stated that you live separately from your brother. We have listed the conditions for sharing sacrifices in the answer to question no. 96741.
There we mentioned the difference of scholarly opinion concerning the ruling on sacrifices, and stated that it is a confirmed Sunnah (Sunnah mu’akkadah) according to the majority and it is obligatory according to a few fuqaha’.
The scholars stated that slaughtering the sacrifice is better than giving its price in charity. Based on that, you can offer the sacrifice and give the meat in charity, or you can delegate someone to sacrifice it on your behalf in countries or regions where there is a great deal of need.
It says in Mataalib Ooli al-Nuha (2/473): Slaughtering the sacrifice or the ‘aqeeqah is better than giving its price in charity. This was stated by Imam Ahmad (may Allaah have mercy on him). The same applies to the hadiy (sacrifice offered during Hajj). The Prophet (peace and blessings of Allaah be upon him) slaughtered his sacrifice and hadiy, as did the caliphs who came after him. If giving the price in charity was better they would not have failed to do that. End quote.
And Allaah knows best.