I'm going to come late to my mothers surprise party
Why are you going to arrive late to your mother's party?
I don't want to go home early because of my father. He is the one who made the surprise party.
It would be impolite to show up to your mother's party late. If you say you're going to be somewhere at a certain time, you should do your best to be on time. If you show up late your mother might be very disappointed.
It's alright. I'll just say it was scheduled late, my father is a liar too.
When you promise to be on time, try to stick to it or at least let the other people know that you can't make it. You shouldn't avoid your mother because of your father. Be there for your mom and she will be happy for your presence.