Hopefully you are within 30 days of entry of the default judgment. If so, you only need to set forth the bare minimum. Go read 735 ILCS 5/2-1301(e). http://www.ilga.gov/legislation/ilcs/ilcs4.asp?ActID=2017&ChapterID=56&SeqStart=15800000&SeqEnd=16400000 . There may be a fee to vacate the order.
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You want everything to be handled then and there . . . but you've never bothered to seek custody prior to this?
Let me make sure I've got this straight: The mother of your child is addicted to prescription medications . . . and you agreed to leave your child with her. The mother of your child attempted suicide . . . and you agreed to leave the child with her. She said she wouldn't seek child support from you as long as you didn't reveal these facts about her . . . and you would continue to leave the child with her.
Then, a support order is entered, and you suddenly realized that you should be the custodial parent.
Oh . . . and you want to do all this without the help of an attorney.
Boy, have you got your work cut out for you.
The most important thing you could include in your motion would be a request for a continuance to give you time to hire a lawyer.
If the order was entered more than 30 days ago the standard for vacating a final order is more stringent. In either case, success on your motion is important due to the facts you set out. Improve your odds of winning by hiring a lawyer now; you will need one for the custody battle too.