I'm with the others. The caps on the output are waaay to big. They may make you think they make your problem better but that is only because the op amp can't drive that much capacitance. As an experiment you could move the 1010 outside the feedback loop by moving the right hand side of the pot to the output of the first op amp. Then the 1010 is just a voltage follower. Maybe a 0.1 ufd on it's output.Thanks for your help.
What I mean, is that my voltmeter will start reading variations (haven't scoped it yet, but I might) in the order of at least ±20mv twice a second, and it also tends to drift... A LOT.
I'm almost sure that the problem lies in the LT1010 chip. Or the way I connected it. Either way, my sim also shows a steady -5V output, but that's not the case in real life.