Domain Admin access within a trusted domain

I apologize if this has been answered, but I can’t find the answer anywhere. I have the admin accounts on two seperate trusted domains. I would like to be able to login into domain B as admin using credintials from domain A. I already added the domain A domain admin group,which I am a member of on domain A, to the builtin Administrator on domain b, which gave me local admin rights to the DC on domain b, but not to any other pc’s on the domain. Is there any way to get admin rights for the whole domain?