dog2k5
I do not understand exactly what you are doing, but
if you define them as two seperate parts, you need to decide what kind of bonding should exist between them: full bonding (Tie) or with interface properties (allowing sliding at the interface)that you should reasonably estimate based on lab results or judgement say.
However if you define them under one part then the nodes are automatically constrained (full bonding).
Refining the mesh is helpful except in only few cases: for example when high distortion exists and one uses Nonlinear geometry then the small element areas will become zero/negative or close to which results in stiffness being zero at the associated DOFs
Sometime the huge difference in the stiffnesses of the two adjacent materials will lead to this situation.
Also in order to get more info about the divergence problem you are experiencing you can go to the msg. file in the job directory