UNAPPROVED SEAT INSTALLATION. FAA INVESTIGATION.

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I FLEW WITH A FRIEND TO PHILLIPPI; W VA; TO PICK UP MY CHILDREN -- 3; 5; 7; AND 8 -- 30 LBS; 35 LBS; 35 LBS; AND 40 LBS RESPECTIVELY. I FLEW A C-172. IN THE PLT'S OP HANDBOOK THE WT AND BAL SECTION DESCRIBES THE INSTALLATION OF A CHILD SEAT IN THE BAGGAGE AREA OF THE CABIN. IT IS TO BE ATTACHED TO THE TIE DOWN POINTS. I INSTALLED WHAT I BELIEVED TO BE AN APPROVED CHILD SEAT WITH STRAPS (2000 LBS TEST) TO TIE DOWN POINTS. ALL ATTACH POINTS WERE METAL TO METAL PER FAR. I CONDUCTED WT AND BAL AND ALL FELL WELL WITHIN THE ENVELOPE. WHEN I PICKED UP MY CHILDREN; MY EX-WIFE SAID SHE WOULD CALL FAA IF MY FRIEND RETURNED WITH ME IN THE PLANE AS THAT WOULD MAKE ONE MORE PERSON THAN SEAT BELTS. I TOOK MY FRIEND TO OHIO TO A BUS AND FLEW MY KIDS TO FFL. AT FFL; 2 REPRESENTATIVES OF FAA MET ME AT THE PLANE AND INFORMED ME THAT THE SEAT WAS NOT THE 'CESSNA' APPROVED SEAT AND THAT THE STRAPS WERE NOT PMA. I BELIEVE THAT PLTS SHOULD HAVE A MORE READY SOURCE OF INFO CONCERNING 'FAA APPROVED' AND 'APPROVED FOR USE IN AIRPLANES.' CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: FAA REPRESENTATIVES WHO MET RPTR'S ACFT TOLD HIM THAT HIS CHILD SEAT LOOKED LIKE A SAFE INSTALLATION; BUT IT WAS NOT AN APPROVED FAA INSTALLATION. THE ONLY FAA APPROVED ONE IS A CESSNA SEAT. RPTR HAD CHKED HIS OWNERS MANUAL AND THOUGHT THE SEAT HE USED WAS ADEQUATE BECAUSE IT WAS A DOT AND AIRLINE APPROVED CHILD RESTRAINT SEAT. FAA IS INVESTIGATING; BUT HAS NOT CONCLUDED.