This paper studies the problem of optimal beamforming and power allocation for an amplify-and-forward (AF)-based two-way relaying network in the presence of interference and channel state information (CSI) uncertainty. In particular, we obtain the beamforming vector as well as the users' transmit powers under two assumptions on the availability of the CSI of the interfering links, namely norm-bounded uncertainty model and the second-order statistics scenario. To do so, we develop two design approaches. The first approach is based on the total transmit power minimization technique. We start with the norm-bounded uncertainty model and derive the optimal solution to the corresponding problem. To reduce the computational complexity, we also develop a low-complexity algorithm which offers performance that is very close to the optimal one. In the second approach, we apply a signal-to-interference-plus-noise ratio (SINR) balancing technique. We propose another low-complexity algorithm based on the SINR balancing criteria. Next, we consider the scenario where the second-order statistics of the CSIs are available. Again we start with the total power minimization method and derive both optimal and suboptimal algorithms. Finally, we apply the SINR balancing technique to this scenario and develop another low-complexity algorithm, which is suitable for practice.