I'd improve the date picker so that the value it posts back is always yyyy-MM-dd but displays in whichever culture you care about. This makes the problem a client problem, not a server one (which it is really)
UPDATE
I've done some investigation Convert.ToDateTime() simply calls DateTime.Parse with the current culture settings. I've just checked one of my VMs and it runs with US local settings which is why your're getting the error you are with d/M/y. I would standarise the format of the date that is being sent to the server (it doesn't really matter to which format, but I'm always a fan of YMD) and then use DateTime.TryParseExact() that @No One mentions, but with just one format.