Random effects of cohort/round

I am using Maaslin2 to compare the gut microbiota of rats born to females exposed to opioids or saline. I have 3 morphine dams and 3 vehicle dams, which are split over two rounds (some vehicle and morphine in both rounds). I had run the analysis using “Mother” (or which dam the offspring came from) as a random effect, but I noticed that there is a difference in the composition of the two rounds. I am only interested in the treatment effect. Should I add another random effect of “Round”? If so, should I replace “Mother”, or use both?

When multiple random effect terms are specified, Maaslin2 uses them as separate varying intercept terms. So in your case setting random_effects = "dam,round" would make the model formula would end up looking like ~ <other terms> + (1|dam) + (1|round). If you have enough data from each dam to support that you should be okay.