But the 28-year-old from Doncaster turned it around and birdied the last to draw level with Mills and Simpson.
Mills, whose only Ladies European Tour victory came a decade ago at the German Open, also birdied the final hole to move alongside the 31-year-old Simpson, playing in the penultimate pairing.
Defending champion Linda Wessberg carded a 73 and slipped to one-under for the tournament. The day’s early starters endured the worst of the bad weather.
But it was talk of The Solheim Cup – the women’s equivalent of the Ryder Cup – that arguably had a greater impact on some of the players.
Hudson, Hauert, Wessberg and Tinning are among those with the greatest chance of qualifying for the European Team.
Top-six finishes at Machynys for Hudson and Hauert would see them leapfrog Annika Sorenstam in the rankings, while a top eight finish would be enough for Wessberg.