So there are two ways you can do this. The first is to use the date range picker component instead, which has this functionality built in. But if you're set on using two date pickers, the date picker component has two settings that you can use:
Minimum date
Maximum date
If you fill the appropriate one in with the value of your other date picker component (and vice versa), that should work.
Here's an example - I set the maximum date of the "Start" date picker to be the value of the "end" date picker (or a date very far in the future if the end picker has no value).