Hi Pollux,
I agree with few responses here, and it's not a big deal if you take a 3 months break from your work.
The adcoms would be fine with it as long as you have a convincing story. But yes, as mentioned by someone else as well
don't just do nothing during that time.
I am and MBA myself (SDA Bocconi, batch of 2011) and also interviewed with 6 schools. To quote one of the examples of my friend, he actually took a break for 2 months from his work and pursued his interest of community service (worked for an old age home). It actually was a great value add for his profile.
Hence, I would say its actually an opportunity for you. As there is a Chinese saying "There is opportunity in crisis". Take advantage of this and work on something you never really could during work. It would help you both personally and professionally. I am sure you can manage sometime even after taking care of your dad.
Hope this helps !
Let me know if you have more questions
Cheers !
DJ