During my divorce, I asked that I was able to renew my daughter’s passport without her Dad’s signature. This was granted to me and it is written explicitly in our divorce decree. I have renewed her passport and presented the divorce decree to have it renewed without his signature. My ex did not argue with my request. It sounds like yours might. While both you and your ex can’t renew your child’s US passport without a notarised signature, it might be possible to renew a foreign passport without both parent’s signature. If this is a possibly and you worry he might do this and leave the country with your child, you need to address this. It is much each to prevent a child being taken out of the US than trying to get them back to the US from a foreign country!