Dates in the m/d/y or d-m-y formats are disambiguated by looking at the separator between the various components: if the separator is a slash (/), then the American m/d/y is assumed; whereas if the separator is a dash (-) or a dot (.), then the European d-m-y format is assumed. If, however, the year is given in a two digit format and the separator is a dash (-, the date string is parsed as y-m-d.
To avoid potential ambiguity, it's best to use ISO 8601 (YYYY-MM-DD) dates or DateTime::createFromFormat() when possible.
By replacing the separator you are telling it to use d-m-y format. If you want either to be handled remove the str_replace.
Use carbon either create or parse. Carbon has this functionality already to take a date string in most formats and create a date object ready for MySQL. And Laravel uses it out of the box.
The date parsing Carbon does is just a wrapper over the DateTime constructor which is the same parsing done by the http://php.net/manual/en/function.strtotime.php function so there isn't a difference in what dates you would get by using Carbon vs. the core php functions/objects. You do get a much nicer / more readable api though so I'd still recommend it.
For more information on what formats Carbon/DateTime/strtotime can handle take a look at the php docs.
