I've got a DESeq2 design matrix question.

I have two groups of mice, young and old.

Mice in both groups have been given of 3 different treatments  (control treatment (treatment zero), and two treatments of interest (treatment1 and treatment2). Some of the treated mice show a response to the treatment, some do not. The control treatment mice never show a response. Some of the old mice do not respond to one treatment.

I'd like to pull out:

1) the DEGs after treatment1 compared to treatment0 in young mice specific to the repsonse
2) the DEGs after treatment2 compared to treatment0 in young mice specific to the repsonse
3) the DEGs after treatment1 compared to treatment0 in old mice specific to the repsonse
4) the DEGs after treatment1 compared to treatment0 in old mice specific to the response
1) the differences between 1) and 3) (i.e. some sort of interaction term)
1) the differences between 2) and 4) (i.e. some sort of interaction term)

I know how to do all of this without addressing the response (i.e. as a simple interaction term based design of ~age+treatment +age:treatment) but I have no clue how to address the response variable and  get only genes that are changing in the the responding mice.

Is there a way to do this all in one design or should I be looking to split it up somehow?

Here's the metadata:

Thanks,
John

And to clarify, do you determine the responder status using the RNA-seq data?