Hi MBA2,
Second MBA is uncommon, but people do that. And for the reasons mentioned by you - career change.
Although your GPAs are low, they are somewhat balanced by your GMAT score. School look at these stats with a purpose, and that purpose is your ability to succeed in a fast-paced, quant-heavy curriculum. And it's not just your GPA that goes into this determination. They look at other factors as well such as reputation of your institution and how rigorous the course was. Anyway, you can't do much about your GPA now. So, no point bothering about it. Instead, focus on your essays.
Second, your post-MBA (immediately after MBA) career goal of PE may be ambitious, because it's extremely tough to get into this industry. I'm not saying you can't, but it's hard. Now, an unrealistic/ difficult career goal in an application (including interview) can work against an applicant, as B-schools are cautious about taking in those applicants who may struggle to get placed. Afterall, placement is probably the most important factor that goes into ranking and their overall reputation.