How to enter the middle initial because my child has more than one middle name

Look at the Social Security card for the child.  If the card shows two middle names then use the initial for the first name listed.

You can only enter one middle initial. But it's not important what you enter. Do what DoninGA said, or you can just omit the middle initial and not enter anything. It's not required.

The IRS only looks at the first 4 letters of the last name, the year of birth and the SS# ... everything else is immaterial.