I have done something very similar. I have a web site that accepts firewall requests. It sends an e-mail to LPM and LPM creates an incident AND a firewall form within the incident and populates all attributes for me. I now have an incident that goes between network, security, network etc etc until everyone is happy. Then I have an action called "Transform to Change" (I thought the process sounded more interesting using the work transform). Below is my process:
Selecting the action causes a "Create Change" but a "Create Incident" should also work. I then auto resolve the incident and move on. Double clicking the "Create Change" opens a Change Window or in your case an Incident Window and you can fill in the values using attributes from the Problem. I then resolve my incident (Problem in your case) with some nicely worded text describes what happened. In both the Incident and change (Problem/Incident) you will see a collection of the other object. So for me, my Incident shows the Change and in the Change I see the Incident. You don't have to resolve the incident (Problem for you) but I like things clean. I end up with an Incident and a Change and their linked.
In my incident's "Open" control in process designer I had to add "Create Change" and in my Change I had to add "Create Incident". I can't see it now but I thought somewhere I had to add a Create Change Child and Create Incident Child. It's been about 2 years and I just don't remember that detail, maybe it's not required. Overall, it wasn't nearly as bad as I would have expected and ended up being pretty easy. I am assuming that this is possible between any two objects, never tested it so no guarantees.