It was a disappointing day for US Open champion McDowell and ex-Ryder Cup captain Colin Montgomerie.
Nine of Europe's Ryder Cup players are in the field, plus captain Colin Montgomerie.
Laird will be joined by Colin Montgomerie, the only Scot to have won at Loch Lomond.
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Scotland's Colin Montgomerie is five over after a 72 and looks likely to miss the cut.
Scotland's Colin Montgomerie geared up for next week's Accenture Matchplay with another top-20 finish.
Previous winners include Tony Jacklin, Sam Torrance, Nick Faldo, Sandy Lyle, Colin Montgomerie and Sergio Garcia.
Europe captain Colin Montgomerie and two of his assistants, Darren Clarke and Paul McGinley, also take part.
Lile finished on four under alongside Colin Montgomerie, who shot 69, and Lee Westwood, who made 71.
And Colin Montgomerie partners Chris DiMarco, both of whom have lost twice in play-offs in the majors.
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Colin Montgomerie, Padraig Harrington, Ian Poulter and David Howell will all line up in the new event.
Dredge shot a 68 before a superb second-round 65 to qualify alongside Colin Montgomerie and Thomas Bjorn.
Scotland's Colin Montgomerie carded a 71 to finish on nine under par in a tie for 28th.
Scot Colin Montgomerie, who designed the testing course, shot a 71 to be three strokes off the lead.
Colin Montgomerie shot 22 under par in taking the individual title at the 1997 World Cup of Golf.
Sweden's Johan Edfors is two behind with Colin Montgomerie is in a share of seventh place on nine under.
European captain Colin Montgomerie said the new schedule would be "tough" but believes the changes could benefit his team.
Darren Clarke, Padraig Harrington, Paul McGinley, David Howell and Colin Montgomerie, who designed the course, were already in the field.
Golf's inclusion was welcomed by Europe's Ryder Cup captain Colin Montgomerie, who spoke to the IOC in Lausanne in June.
English pair Mark Foster and David Lynn lead the European charge on five under, with Scot Colin Montgomerie two under.
Paul Lawrie, Stephen Gallacher and Colin Montgomerie all finished one better off than Drysdale on six under par for the week.
Colin Montgomerie had been out earlier in the morning to complete his second round after thunder storms delayed play on Friday.
Earlier, Colin Montgomerie needed only two shots to advance to the second round, after beating American Dennis Paulson two and one.
Scotland's Colin Montgomerie is four shots back after a second straight 68.
Carton House Golf Club is Colin Montgomerie's first course design in Ireland.
Pugh, who once coached former European No. 1 Colin Montgomerie, accepted the apologies and called Bradley "classy" for admitting his behavior was wrong.
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Meanwhile, Colin Montgomerie looked haunted by his off-course problems as the European Ryder Cup captain endured a dismal start to his third round.
Not since Colin Montgomerie in 1999 has any player won both the PGA title and the World Matchplay title at the Surrey venue.
Colin Montgomerie was six under after 12 holes but was rocked by a double bogey at the 14th and ended with a 68.
Skipper Colin Montgomerie said the call was "motivational" but also "sad", as Ballesteros is still recovering after operations to remove a brain tumour.
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