I agree with putting it on your resume. This is great experience if you can be honest in your self reflection. Ie realize remote only is probably not a good idea for your first job out of school. Realize that you’ll need mentorship. Etc.
I have no problem leaving the job off the resume (“resumé” means “summary” not “comprehensive”). If asked you could say that you listed all experience that you felt was relavant. But personally I think it is a valuable thing to have listed.
However, I strongly discarded with the parents suggestions for “massaging” the resume. Those sugggestions are pure lying. There is a big difference about highlighting certain aspects of a career and stating things as fact which are not true.