This is happening in a custom feature you are developing right? Not an existing mojoPortal feature?
I do know of some quirkiness in the jsCalender under IE but not the kind of thing you are describing.
There is another DatePicker you can use by referencing the ajaxtoolkit from the _libs folder. You basically use a TextBox and an extender control to make it DatePicker like this:
<asp:TextBox runat="server" ID="txtEventDate" />
<ajaxToolkit:CalendarExtender ID="ceEventDate" runat="server" TargetControlID="txtEventDate" />
In code you can set the date format like this:
ceEventDate.Format = CultureInfo.CurrentCulture.DateTimeFormat.ShortDatePattern;
Hope it helps,