Searching between dates on a CHAR type field
You can cast your date to perform where clause on it just like this.

WHERE CONVERT(DATETIME, MyStringDateField, 120) BETWEEN @DateParam1 AND @DateParam2


The last parameter in CONVERT is the date format. You must choose the one that match your text data of your date. You can find the list here

You must be aware that if a string does not match a date for a particular record, your query will fail with a message saying that the data XYZ cannot be converted to DATETIME type.