Multiple comparisons on a net response formed by two independent responses

I have a group of organisms to which I apply a number of treatments (N). For half of the organisms to which I apply a treatment, I measure response y1 (effect) and for the other half I measure response y2 (control). Part of the responses later appear invalid and are discarded, resulting in unequal sample sizes. For each treatment, I am interested in the net response y1-y2 (difference between effect and control measurement). Note: These two responses are not paired, as they are measurements performed on different organisms and have both error within and between treatments.
My two questions are the following:
  • Which (omnibus) test should be applied over all treatments? Up till now, I have done an ANOVA putting in both treatment and control/effect as independent variables, but this does not strike me as correct.
  • How do I do the multiple comparisons/post hoc? I only need to compare between the null treatment (n=1) and the other treatments (n=i), like a Dunnet's test. Up till now, I have made 95% confidence interval of y1-y2 (using the 2-sample independent t) for all treatment groups and then compared which, but this does not sound 100% right either and loses quite some power (and runs into p-adjustment).
I work in R to perform my analyses, in case that is relevant. I have seen stuff about mixed models and longitudinal models but I am not sure if that is what I need and how it applies here.