Amy Duggar King's amending her earlier statement in which she showed support for Kendra Duggar ... telling TMZ she's now only standing in solidarity with the children involved.

We spoke with Amy -- Joseph Duggar's cousin -- after Kendra was arrested for child endangerment and false imprisonment.

If you don't know, right after Joseph was arrested and charged with lewd and lascivious conduct with a minor, Amy showed support for both Kendra and their kids in a statement.

Amy -- who wrote a book about her time around the Duggar children titled "Holy Disruptor: Shattering the Shiny Facade by Getting Louder with the Truth" -- says she's now just worried about the kids ... both the child Joseph allegedly assaulted and Kendra and Joseph's four children.

She adds she hopes Joseph and Kendra are held accountable for their alleged actions.

As you know ... a 14-year-old recently came forward and claimed Joseph molested her when she was 9-years-old in Panama City Beach, Florida.

At the time of his arrest, Amy also said she was "not surprised that another alleged predator has emerged from this toxic system."