Once you have returned the dates from the URLs then you can add to the date values and then append back the rest of the URL using the '&' symbol or CONCATENATE function.
The challenge, then, is to extract the date strings whereby there are several possibilities:
If the URL is always the same length before the date string then a simple MID function will do it. In your first 'Kayak' URL the function =MID(A1,102,10) gets the first date assuming the URL is in cell A1. If the length changes but not by much then the start character position (in the example at 102) can be found such as using the find function =FIND("/",A1,80) which returns 101 so 1 has to added within the MID function.
The Text to Columns menu item to split each URL by the '/' or '=' character thereby extracting each part including dates.
Some VBA code could be used to analyze the URL structure and perform the required changes.