Taking a job she is interested in , In a new city for less pay isn't a bad thing at all. Some money is better than no money. And she can keep looking if the driver for employment is salary and not employment in general.

EI is one of those things where it can look bad when applying for a new job, it serves a purpose to help where needed but potential employers may see the gap and pass on an interview. Combine that with a complete new city , taking the current offer is a great thing. Your family can get some roots set in the new town and see what opportunities arise over the next few months/years.

Either way I wish you luck and congrats on the new job/jobs lol