Você precisa escapar do caractere CMD especial &
prefixando-o com caractere ^
Isso deve funcionar
@echo off
set "_link=https://mywebsite.com/something/morething/abc.html?checkin=2018-07-21^&los=1^&adults=2^&rooms=1^&cid=-1^&searchrequestid=68159c43-71a5-4dc9-9cb1-35a82ed8e8d8&tabbed=true"
START %_link%