How do I select a proper design matrix to use in DRIMSeq?
From your question I understand that you have two treatments in two mouse strains.
If you are interested in general treatment effects independet of the animal strain you would use the both variables in the design formula (similar to controlling for a batch effect).

meta.data &lt;- data.frame(treatment = c("a", "a", "b", "b"), strain = c("x", "y", "x", "y"))
design_combined &lt;- model.matrix(~ treatment + strain, data = meta.data)


If you want to make the comparisons for each strain separately, the easiest way will be to split your data set by strain and do a set up just for treatment. Alternatively, you can also merge the two columns into a new one in case you also want to also compare between the strains.

meta.data$combined &lt;- paste0(meta.data$treatment, "_", meta.data$strain)
# refactor to change the reference level
meta.data$combined &lt;- factor(meta.data$combined, levels = "bx", "by", "ax", "ay")
design_combined &lt;- model.matrix(~ combined, data = meta.data)


To get the fold changes, you can extract the proportions for each transcript using

DRIMSeq::proportions(dataSet)


And from the proportions the log2 fold changes can be calculated with ease.

However, when I look at your plot something seems very off with your analysis right now. In all the examples I have seen and also in my own data the diamonds are representing the mean proportion of a transcript in a condition. See this example from the DRIMSeq manual on Bioconductor:
 

In your case there are several different means per group and if you look at the line to the very right the two treatments seem to be to be right on top of each other.
So I think that treatment and strain are somehow mixed in your setup and this is causing this kind of merged plot. If you use a design as outlined above you should get much better results. Additionally, you could maybe check that the meta data is correct.

Also in case you have not read it yet, the manual is a great resource:
https://bioconductor.org/packages/release/bioc/vignettes/DRIMSeq/inst/doc/DRIMSeq.pdf