Which fixtures should I apply to this model?

Hello, I'd like to simulate quite simple thing - two levers acting at each other in housing. I tried a few times with different options but I can't do it realistic. In real life the bigger lever would open the lesser one, so at first I tried large displacement option and sparse solver, but now I just want static reactions in pins and levers in the moment when levers are clatched together. Attached you can find my last results and my main problem - which fixtures should I apply to plain bearings (pin and lever connection)? As you can see lesser lever displaced over 1.5 mm despite the component contact no penetration. I even plotted the pressure contact and you can see pressures on bigger lever's pin, but they're absent on lesser lever. Somethings clearily wrong, can anyone help me?