A simple fix in your particular case is just to do Module12(Module2, Module1) to make the order go to Mod2 first and then Mod1:
from torch import nn

class Module1(nn.Module):
    def __init__(self):
        print("Mod1 entry")
        super().__init__()
        print("Mod1 after super")
        self.l1_loss = nn.L1Loss()


class Module2(nn.Module):
  def __init__(self, damy):
    print("Mod2 entry")
    super().__init__()
    print("Mod2 after super")
    self.damy = damy

class Module12(Module2, Module1):
  def __init__(self, damy):
    print("Mod12 entry")
    super().__init__(damy)
    print("Mod12 after super")

print(Module12.__mro__)
module12 = Module12("damy")