Praise be to Allah.
We do not think that you should enter this program, because of what it involves of looking at women’s ‘awrahs unnecessarily. Allaah says (interpretation of the meaning):
“Tell the believing men to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts). That is purer for them. Verily, Allaah is All‑Aware of what they do”
Rushing to graduate is not regarded as a case of necessity, even if it is for the sake of serving your father. You can reconcile the two interests according to what you are able to do. You can appoint whoever you think is suitable to do this service, even if it means paying them, if there is no one in your family who can do it for free.
We appreciate your eagerness to serve your father and we appreciate your keenness to adhere to shar’i limits. We ask Allaah to decree for you the reward of that, and we ask Allaah to decree a speedy recovery for your father, and to give him both reward and well being.
And Allaah knows best.