I have an RNA-seq experimental design which includes replicates that are not exactly technical replicates and not exactly biological replicates. I compare tumor samples, but the same tumor is implanted sometimes in two or three different mice (and sometimes in just one mouse). So, let's say the sample matrix is something like this:

   PATIENT| MOUSE | GENOTYPE | TREATMENT_RESPONSE
    ------ -------  --------- -------------------
      A   |   1    |   WT     |  TRUE 
      A   |   2    |   WT     |  TRUE 
      B   |   3    |   MUT    |  TRUE 
      B   |   4    |   MUT    |  TRUE 
      C   |   5    |   WT     |  FALSE 
      D   |   6    |   MUT    |  FALSE 
      D   |   7    |   MUT    |  FALSE 
      D   |   8    |   MUT    |  FALSE

I want to compare the genotype (WT vs MUT), and also to compare the treatment respone (TRUE vs FALSE). Two samples from the same patient in different mice are not technical replicates so I can't collapse them but also not really biological replicates because it's the same tumor. Also, some patients have one such replicate, some two, some three. Will controlling for PATIENT (e.g ~PATIENT + GENOTYPE or ~PATIENT + TREATMENT_RESPONSE) solve the issue? I saw two different posts, one suggesting such a thing, the other suggesting not to use DESeq2 and instead to go for limma-voom's duplicateCorrelation. Which is more fitting in this experimental design?

Thanks!

The "controlling" designs won't work due to confounding. Look at the table and see how they are linearly dependent (if this is not clear I'd recommend chatting with someone at your institute about linear modeling and confounding).

On the support site I have recommended duplicateCorrelation and limma many times for these designs.