Is it appropriate to use estimated marginal means when model estimates are not significant but data is unbalanced? Is it appropriate to use estimated marginal means when estimates (either interaction or main effects) are not significant but the data is unbalanced? I've come across variations of this question on stackexchange (e.g. here), but can't seem to find a definitive answer. Is it dependent upon the particular circumstance (so no right or wrong?). If it is dependent upon the circumstance, hopefully you can help me understand if my approach is fine. In my example, I have a linear mixed effects model (using lmer in R) which I test for differences in offspring body mass between treatments and years. It looks like this:
lmer(bodymass ~ year*treatment + (1|mother.id)

Each mother has several offspring, and some mothers appear in both years. The p-values for the 'year x treatment' interaction, as well as the main effects of 'treatment' and 'year' are all non-significant (alpha > 0.05). Visually, it seems like there is a true biological interaction that I'm not detecting statistically (see plot below). The plot shows the predicted estimates from the model with 95% confidence intervals; sample sizes (i.e., # of subjects) are as follows: Control 2017 = 12, Treatment 2017 = 7, Control 2018 = 18, Treatment 2018 = 19). 
Because it looks like there may be potential for a type II error, I calculated the estimated marginal means from the model (using the emmeans pkg). I ran two t-tests to compare the em means (control 2017 - treatment 2017 and control 2018 - treatment 2018), and found that the 2018 comparison was significant (p < 0.001), but not the 2017 comparison. The em mean interaction plot looks similar to the predicted value interaction plot below. I'm guessing that at least part of the reason I don't find a year x treatment interaction in the model is due to imbalance between the years (removal of outliers does not change p-values greatly in original model), so would it be appropriate in this circumstance to use estimated marginal means for reporting pairwise difference from the model? It would also be useful if someone could provide me with an academic reference that discusses how/when marginal means can be used.

 A: People seem to have an assortment of pretty rigid practices. I'll just comment that I think ANOVA F tests are kind of overrated. They can be useful for deciding what model is suitable for a dataset; but they do not help much, in my opinion, for doing any meaningful inference. 
In particular, if you have fitted a two-way factorial model including interaction, and the residual diagnostics look good, I don't see anything wrong with proceeding to do post hoc means and comparisons without even looking at the ANOVA table. Appropriate multiplicity adjustments should be used, and I think it's important to look at the means themselves, not just the pairwise differences -- both from a subject-matter perspectives -- and probably plot them as well. 
I am a lot more comfortable with what is described in the preceding paragraph than I am with some analysis where rigid rules and "significance" criteria are applied, but no diagnostic plots or descriptive plots are examined. I see this kind of routinized method way, way too often.
Not only do I think that little is lost by ignoring ANOVA tables, it is possible that something will be gained. For example, suppose that in skipping the ANOVA and plotting the means, we observe an interaction that would be of scientific interest (but for which there is insufficient data to achieve the magical "P < 0.05" threshold). (is that the situation in the posted question???) This would suggest something potentially important that could be investigated in further experimentation. A devoted user of ANOVA tables may summarily throw the interaction out of the model, hence never having the opportunity to notice this potentially important result. Remember, just because something isn't "statistically significant," that doesn't prove it isn't there; it just means you don't have enough data to be sure it isn't part of the noise.
