parallel execution issues when framework has dependency of library testcases on other testsuite

678,

Thumb rule is each and every test case has to be independent.

The information available is not sufficient to comment why test cases are failing. You haven't mentioned either what is causing to failure.
Also, not sure what sort of data that are being supplied to other test cases.

Is possible to create a sample project to replicate the issue?
Does the sequential execution work fine?
Reason for executing them in Parallel?