Sometime back, I was trying to connect 2 saleforce org via Oauth/Rest API.
I think I did something similar.
On Salesforce org(Source) act as auth provider. I created connected app in Target org to finally get the Oauth Token.
providing small code base for that:
String reqbody = 'grant_type=password&client_id='+clientId+'&client_secret='+clientSecret+'&username='+username+'&password='+password;
// All of these u'll get once you set up connected app
Http h = new Http();
HttpRequest req = new HttpRequest();
req.setBody(reqbody);
req.setMethod('POST');
req.setEndpoint('https://login.salesforce.com/services/oauth2/token');//Note if my domain is set up use the proper domain name else use login.salesforce.com for prod or developer or test.salesforce.com for sandbox instance
HttpResponse res = h.send(req);
OAuth2 objAuthenticationInfo = (OAuth2)JSON.deserialize(res.getbody(), OAuth2.class);
//RequestWrapper reqst=new RequestWrapper();
if(objAuthenticationInfo.access_token!=null) // your check for access token
{ for any further Rest API call, I was using this, which I think you needed:
**req1.setHeader('Authorization','Bearer '+objAuthenticationInfo.access_token);**
--------your further code------ }
Let me know in case you've any doubt over this :