MBUGS, a few tings to consider here.
-A 3.5 trainer kite is about as big as a trainer kite gets. This means it's designed only for light wind flying i.e. below 15 knots (27 km/h)
-Wind strength is one thing but wind quality is another. Flying a kite in a park is typically where you find the poorest quality of wind due to obstacles around (houses, trees, hills, etc.) interfering with the wind, thus creating turbulence in the wind. The wind meter you read is most likely in an open area away from obstacles, so if it had 16 km/h of variation in it's in reading, you probably had even more variation in a park, plus the way you described your experience it seems the wind was changing direction, and I'm guessing this is due to the obstacles around you.
This video explains some of the basics on wind effects:
-Trainer kites are ''non-depowerable'' kites which means you are mostly at the mercy of the wind and all it's power is held by your arms. The feeling you will get from an inflatable ''depowerable'' kite will be very different and will require some adjustments. As said before a 3.5m foil kite probably pull as much as a 6 or 7m inflatable kite.
My advice is to avoid flying this size of trainer kite beyond 30 km/h, especially if the wind is of poor quality
My other advice is to get your hands on the kitesurfing beginner progression DVD which will cover many essential basics and safety concepts and will facilitate your progression when you book lessons.
Stay safe,
Christian