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.
Praise be to Allaah for giving you what you wanted; and we ask Him to permanently shower His favor on you and make you grateful to Him. Now you are required to fast five days and slaughter two sheep. As for the fast, its ruling is clear to you. As for slaughtering, you are required to fulfill the vow according to the way that you specified. Paying the price of the sheep, instead of slaughtering them, does not absolve you of your liability. You can either slaughter them by yourself or authorize someone to do so on your behalf, whether that is your brother or a relief organization or anyone else. It is permissible to do this both in your home country or in the country where you live. It is also permissible that your brothers eat from the meat because they are poor, as you mentioned, and because they are not among those whom you are responsible for in the Sharee'ah. If your mother is alive and they gave her a part of the meat, then this is also permissible. However, you are not permitted to do this, because according to the Sharee'ah you are required to provide for her.
Allaah Knows best.