What exactly is your GET button doing? Is it editing a record? Inserting a new record (and thus changing the [Maximum Record ID#])?
If [Maximum Record ID#] is a summary field, and you already have access to that summary field from your child record (by looking up the summary field in the parent table), you can insert that [Maximum Record ID#] directly into your URL (to indicate record to edit).
Can you try the following and let me know what you find:
Put the [Maximum Record ID#] as a column in your report. Then let me know what happens to the [Maximum Record ID#] - before and after you hit the GET button, etc.
From what I've seen, the [Maximum Record ID#] updates right away on refresh - so there's something I'm not understanding about what your app is doing.
Please also outline your table structure - the parent, child table, where the GET button is, what it's doing, etc.
