You didn’t tell us if your problems occurred while planing or schlogging. Are you in the harness & footstraps or just using the harness?
I have to totally agree with Roger on this issue. Two things make the board turn up wind, windward rail pressure caused by too much heel pressure, or moving the center of effort (CE) of your sail behind the center of lateral resistance (CLR) on your board. Too large a fin will only make you tail walk.
While your fin obviously needs to be changed because of your water depth-I would tell your dad it is a safety issue-the 42 cm fin is not so large as to cause to cause major problems unless you were really powered up.
One issue I would address is your sail & board size if you are planing. You didn’t tell us what your 130 liter board was. Many 130 liter boards don't work well with sails smaller then 6.5 so a 6.2 sail may not be optimal for your board especially at your light weight. With too small a sail in planing conditions the board becomes very nervous forcing you to sail defensively. A normal reaction to sailing defensively is to apply too much heel pressure which sends you up wind. Also, if planing conditions I would not recommend you consider using a 130 liter board with a 5.0 sail. If 5.0 & 6.2 are your normal sail sizes you may want to trade your current board for a smaller board.