PA-30 trainee reported on departure experiencing an asymmetric flap issue resulting in a uncommanded roll. The Flight Instructor took control of the aircraft and landing safely at the departure airport.

Narrative

In pursuit of an additional rating (Multi Engine Land); I experienced challenges coordinating both an aircraft and designated pilot examiner (DPE) and elected to travel out of state to complete my training in the same type of aircraft (PA-30) at a location that had both the aircraft and examiner available. For context; I work in a day job which constantly balances risk management. My experience training for this rating paired me with several young time building (airline seeking) MEI instructors; to which I found myself regularly challenging my no-go criteria; CRM; and aircraft airworthiness.Traveling out of town provided for a fairly narrow timeframe to complete the training. My preparation was split over two trips; and while completing my final practice flight the day before the scheduled checkride; I was challenged in aeronautical decision making (ADM) and external pressure. The straw that broke the camel's back related to an asymmetric flap and maintenance issue. Upon retracting the flaps at <100AGL on a short field takeoff; I was found quickly countering an uncommanded roll at low altitude. After notifying the instructor; he stated 'my controls' and lowered the flaps to match while telling the tower we had an issue. However; he attempted (not once; but twice) to retract the flaps back up unsuccessfully as I found myself uncomfortably trying to mention that it was not advisable to do that in the pattern. I was taught to not make things worse when in a stable condition. After a successful return to the airport and taxiing clear of the runway; the flaps retracted and the MEI suggested we finish my practice flight. Because we had a serious issue (asymmetric flaps) I suggested that we go back and look at the aircraft because if they didn't retract under aero loads a few minutes ago; they might not retract when up at altitude. Begrudgingly; he agreed and we went back to investigate. After shutting down the aircraft; I released the brakes and the aircraft rolled backward on the slightly sloped surface followed by a clunking noise. While the instructor was busy on the phone with the flight school owner discussing how to lube the flaps tracks (evidently this asymmetric flap issue happens once a month); I was looking at the aircraft for the source of the clunking noise. Once lubed; we pulled the aircraft out of the tiedown spot and I had to convince the MEI to let me push the aircraft back and forth with the towbar to investigate the noise. After pushing the aircraft back and forth a couple times; we heard a loud clunk and it soon became apparent that the left main landing gear was cracked and likely about to fail. Caked in layers of grease and exhaust soot; the crack may not have been apparent on a cursory inspection; but the landing gear casting now was dislodged next to the trunnion. In addition; a weld was noted near the crack area; which I suspect was likely not an approved repair. Further inspection also revealed numerous loose rivets in the wing spar and landing gear area.Throughout this process; I had pointed out (politely questioned) several concerns to the flight school owner and MEI regarding rivets working loose on fairings and lower wing panels; to which they were shrugged off. One response to the rivets was 'What's the worst that could happen?'; to which I was flabbergasted. In addition; it seemed like I was challenged as to why I was doing thorough pre-flights on an aircraft that regularly flies and had no issues reported.The scenario of CRM in the cockpit reminds me of the young first officer trying to alert the senior captain of something being amiss; yet I was the higher time pilot in the left seat under instruction with more real world experience. Because I was not PIC for the flight; it was indeed the MEI's ultimate responsibility for airworthiness; however I felt like my voice was dismissed at times because I was the 'student'.In summary; I talked myself into flying an aircraft that I shouldn't have and pushed my personal limits. In retrospect; I believe the aircraft was un-airworthy due to the number of worked and pulled through rivets I found after the landing gear issue. In my opinion; the aircraft was not being held to satisfactory airworthiness standards and was being flown by unsuspecting pilots. Was the aircraft adequately cleaned during 100hr inspections to reveal these issues? Did they close a blind eye to the working rivets? As an A&P; and CFI; I should have refused to fly the aircraft; but schedule pressure; Flight school/MEI's normalization of issues; and being 'so close' to a checkride allowed me to put myself into potentially dangerous positions. I do believe this scenario enlightened the young airline aspiring MEI as to listening to the aircraft when it is talking to you and hopefully it carries over in his career. In my case; I was challenged by the IMSAFE/PAVE checklists and successfully re-evaluated this flight scenario after the flap issue. Had we not stopped to look at the flaps; the outcome of the day could have been different if the landing gear failed on a subsequent landing.