As a Veteran who is married to a Veteran (Retired) with one child in college part time and another who is a rising senior getting ready to apply for schools:
I do not know of actual things that would help with the application process for a dependent child (but I will be watching this thread in case there is something I do not know about).
If using benefits to pay for school- there are many ways to get potential instate tuition rates at many public schools.
There are also exceptions for instate consideration if/when PCS’s occur at certain times during your high school education.
This will require a bit of looking into since many places have slightly different rules/needs to be meet.
As for an actual leg up over the competition- dependent children often have plenty to choose from when it comes to essays about overcoming hardships. But that is all that I can think of at this time.