Hi Robert,
Thanks for reporting this. I think there is some JS conflict. The calendar picker does not use jquery-ui library.
The styling for the calendar comes from the plugin itself like below.
<link rel="stylesheet" id="ancr-datetime-css-css" href="http://test.com/wp-content/plugins/announcer-pro/admin/js/datetime-picker/jquery.datetimepicker.min.css?ver=6.2" media="all">
Can you please check if some other plugin is disabling or overriding this CSS?
Thanks,
Aakash