Hi Gaëlle,
From my perspective as a user I can tell the following:
1. Indeed, approaching the full representation of paralogues of a gene family in each species, in theory, might improve the accuracy of gene history inference through reconciliation.
2. Sequences of pseudogenes are less evolutionary constrained and, thus, might be quite divergent relative to those of their functional gene counterparts. This means that adding pseudogenes might bias estimation of phylogenetic likelihood of a tree, in result negatively affecting the accuracy of reconciliation.
So in general I would recommend against including pseudogenes in reconciliation. However, it may depend on the details of your study and it is always possible to use both approaches (with and without pseudogenes) and then to compare the results.
Of note:
Considering your using DNA sequences, you probably study some quite recent events within a single genus or a family of species (otherwise, why not using usually more informative protein sequences?). While it is still relevant to use reconciliation, at such scales (like within a genus) the impact of processes like gene conversion and incomplete lineage sorting becomes apparent and it should be kept in mind that these processes are not modeled in GeneRax or AleRax.
Best regards,
Stepan