We don't even know what, if anything, is presently pending before the court. Perhaps the delay is that you have not yet been able to accommodate the home study. If you wish to expedite the resolution of whatever happens to be pending, or to raise issues that you want resolved that are not yet pending, it would seem sensible for you to retain a lawyer in the state in which the litigation is occurring.

You have told us nothing about the so-called "liability suit" - that sounds like a matter separate from your custody action. If you have been sued for money damages, it would be sensible to consult a lawyer about that lawsuit.