Without knowing your specific research question(s), I can only give a general reply to your query.
At first blush, it seems as if SEM is the framework for you. I would suggest retainining the DV at time 1 as a predictor for DV at time 2 (moderator at time 1 could be hypothesized as potential influence of DV at T1 and DV at T2). Since you mention multiple moderators, perhaps you could discuss your research with someone locally, so that you'd be surer of coming up with a defensible analytic approach that would address your research aims.
As David Morse says, without knowing what the causal models that you underlying your data and aspects of the variables, it is not wise to including anything. A great reference is http://meehl.umn.edu/sites/meehl.dl.umn.edu/files/084nuisancevariables.pdf . Some untrained people think it is appropriate to through every into the model and pretend that the word "control" actually means what it means in English (it doesn't). There has been a lot of work by Pearl and others on how to choose what to control. See http://bayes.cs.ucla.edu/jp_home.html for example.
based on what Daniel mentioned (the Pearlian, or better: the graphical approach), this paper might help (actually I haven't read it yet but it's on my list as I am facing the same issues:
VanderWeele, T. J., Jackson, J. W., & Li, S. (2016). Causal inference and longitudinal data: a case study of religion and mental health. Social Psychiatry and Psychiatric Epidemiology, 51(11), 1457-1466. doi:10.1007/s00127-016-1281-9