Don't know how to handle personal problems outside of work

So I'm a year in to the job now. I'm doing fine and want to grow in my career. The way life goes, there are ups and downs that come with life, of course. Recently my parents are having to decide if they want to operate on or put down our family dog of many years. My dad is having issues with his health, not overly serious, but enough to make me really worried. It's hard for me to keep grounded, I find myself disassociating from the problems, responding more with dismissal and anger sometimes, because I don't feel like I have the capacity to actually deal with them. It's hard especially coming home from 13 hours at work and then talking to my parents and getting emotional over all the issues going on in our personal lives. I don't really know how to manage, I'm still 23 years old and wish I had the life experience to deal with it. I don't want to ignore, but I can't practically get too involved. Feel like I'm becoming a worse and worse person slowly over time, because I'd rather use my free time working out or going out on dates or with friends instead of going home and getting stuck in a mindset of worry. Any one else been here?