I actually work in this field, so I can encourage you to do some further reading and get to grips with the terminology. "Indo-European" remains among experts the most popular way to refer to the entire language family, Anatolian and non-Anatolian. Terms like "Nuclear IE" and "Core IE" are often employed to distinguish the non-Anatolian languages.
"Indo-Anatolian" for the higher-level family is a term that some may use here and there, but no expert would ever make a "well, acktually..." remark as you just did to those in a discussion, professional or layman, using "Indo-European"
"Indo-Anatolian" for the higher-level family is a term that some may use here and there, but no expert would ever make a "well, acktually..." remark as you just did to those in a discussion, professional or layman, using "Indo-European"