It is much more difficult for Real Madrid to win La Liga and Copa del Rey titles now. First, they have several key players injured. As a result, their performance is likely to degrade somewhat. Barcelona is Madrid's main rival for the second La Liga and Copa Del Rey titles. It is difficult for Madrid to win against Barcelona. Madrid has lost four of their last five matches against Barcelona. I would say Real Madrid should focus more on Champions League matches only. If they can continue in the Champions League, Madrid has the possibility to become champions.
Real Madrid don't mind much about Coppa del Rey but because their next opponent is Barcelona, they will try to beat Barcelona even Coppa del Rey is not their priority. It is kind of request from their club pride and they feel being beaten by Barcelona is something too bad and unacceptable in any condition.
No doubt that Real Madrid will spend the best they have for Champions League that is their rest biggest competition and also the one they have best chance to win in this season.
Their main focus may already be on the Champions League. but Real Madrid will definitely continue to fight for their best, be it in Laliga or in the Copa del rey. even now I think Real Madrid will try to win in the Copa del rey. because if the Laliga title is already difficult for them to win then they certainly don't want to waste their opportunity in the Copa del rey. even though they lost the first leg. but a thin score will not be too difficult to turn it around in the second leg. But Real Madrid does have several injured players so their performance may indeed be a little disturbed.
Fact is if Real Madrid beat Barcelona, they will come closer to Coppa del Rey cup and it can be a small achievement for them in Spain after losing La Liga to Barcelona. In La Liga, after unlucky defeat in El Classico, Real Madrid mostly surrender the league to Barcelona.
In addition, with some injuries in their squad and with pressure from Champions League, Real Madrid will avoid losing unnecessary resource for La Liga. They will just play well enough to secure their second position and don't chase Barcelona hopelessly.