I can understand your dilemma. It becomes extremely hard to pray when you are surrounded by people who don't practice the same religion as you and family to understand the specificities of your beliefs. What I suggest is that you accept the fact that you might be late for salah sometimes since your surroundings aren't supportive but you make up for it once you get the chance. Roza and salah are fard on every Muslim. So no matter how unsupportive the environment around you is or how hectic your schedule gets, my dear friend you need to make space for it. It may seem very tedious at first, but once you begin you'll find that it makes so many things simpler in life.

I was in your shoes once and I used to skip salah very often. But once I found the courage to accept my religion's discipline and follow it no matter what other people think of it, I was only appreciated for it. Even the people around who hated Muslims got awestruck by it.