Don't tell your current employer! It's none of their business and if they thought you were looking elsewhere they could fire you. Update your resume, write a clear, concise cover letter and apply for the other job. If you get it, then you give notice.

Dont think twice about looking after yourself and your family. If you're miserable, you're better off in another job. It will be better for your current employer to have someone who wants to work there as well. So everyone wins

Good luck