I think most of the instructors (as you can already see) who would respond to this on this site would echo the same thing about getting a respected national certification.
I do understand that you are probably doing a cost/benefit analysis in your head, and if your hope is to teach one class at one center you are wondering whether the extra expense is worth it. I actually know a number of people who are not full time fitness instructors, but they still get certified and keep up their CECs.
A national certification is now pretty standard in the industry. There are some organizations, like the Y, that run their own training programs, which they use as an option to having a national cert. However, most places want something like ACE or ACSM.
So part of the issue is this place may be willing to accept this, but if you want to teach elsewhere it may not be enough. Also there is a question of insurance…. Are you being hired as an employee, or as an independent contractor? You need to see if their insurance will cover you, and if it doesn’t you need to see if you can buy insurance with the certification you get. Accidents can happen and it is professional responsibility to make sure you are covered.
Mentoring is a good idea. Team teaching lets you hone your skills.