annulment and child custody

Hi. i would like to seek advice regarding annulment and child custody. I've been separated from my husband for almost 5 years already. We have 3 kids. For 7 years of being married, i never been happy with him because of his insensitivity and carelessness. Which drag me to find happiness and care to someone else. My Husband worked abroad but before he left,our marriage is shaky already then after a year i decided to tell him that we need to separate because i'm in love with someone else.He did not say anything. He just accept it as if he doesn't care at all. I did not see any sadness in him when i told him that.
I already have a partner right now and i have a 2 year old son with my partner. But despite of my separation to my husband and living with another guy. i never neglected my children though they are living with my parents but every now and then i go there to check on their needs and see how they are doing. My 3 children also know and close to my partner and considering him as their 2nd dad.
My husband is now going to file annulment. I told him that i will no longer appear in court to be able to make the process fast.but i worry on the custody of my kids. Their age is 7, 11 and 13. I don't want to lose my kids. Is there any chance of my husband gets the custody if i won't appear in court?. What will happen with my kids custody? please help me understand this case. thanks so much.