travels fairly frequently and have faced no issues on re-entry, <<<<<<<<<
Travel is totally different from not living in the USA, it seems that none of this family currently lives in the USA. The question about how long the absence is is key. OP indicate the kid needs to be in the USA for her GC status so it is fair to assume that this IS an issue now. One ornery CBP officer is all it takes to create a problem if the child is the only English speaker giving truthful answers about where she lives.