Two pre-MBA PE jobs? Advice please.

"I got my foot in the door via a family connection so I just don't feel like I could work here anymore after the standard 2 year associate program."

Couldn't you view this the opposite way? Like if my family friend had enough influence to get me in the door, then I'd feel pretty protected and that someone would have my back as long as that person still works there.

Ignoring that, sure, it's definitely still valid to want to move to a GE fund for your own reasons. GE firms tend to be a little more open to non-traditional backgrounds (or at least, Summit and TA and their various spinoff incarnations tend to be, since they're focused on sourcing - doesn't require any particular technical skillset). However, my main concern would be about timing - most IB groups are OK with their analysts recruiting ahead of time, but your PE firm may very well not like that. If that's the case, then you may want to focus on lateralling off-cycle in a few months, since it would be for an immediate start. That might mess with your MBA app schedule though.