The minimum and basic qualification for someone to get an Assistant Professor post is to have a,
1. Master's degree with at least 55% marks.
2. Qualified NET exam in the particular subject in which you have done your Master's degree.
3. The additional experience in the respective field would be an added advantage.
One of the key points could be that there are various stages prior to recruitment. After qualifying NET/JRF, one can initially opt for Guest Lecturer, Ad-hoc Lecturer or a Permanent Lecturer.
This is to be noted that for different Institutions and Organizations, the eligibility criteria are based on their SOP (Standard Operating Procedures) and this could vary from one Institutions and Organizations with other and therefore this can possibly be the case wherein one set of terms and conditions can be found to be negligible but to others this could be the different case.
What the UGC has stated can rule on the government administered institutions but may not work for all private Institutions and as a matter of fact you can't force them. From what you have asked in your query, you mention that, "one of the business school raised the doubt that part time MBA
is not valid for college teaching jobs", gives us an impression that this hasn't been the case with all the applications and therefore as a suggestion may I request you to pl. list out the Business Schools and the Management Institutions wherein this is not a limitation in processing of job applications. You can simultaneously do PhD/Doctorate as well to make your profile more promising.
In addition, there are numbers of private Institutions and Organizations and the business schools wherein the professional requirements may match, and you can use your talent in order to pursue your career through full time or part time jobs. If you broaden your area, then there are other possibilities of carrying on with private coaching in order to have good earnings but then it would be up to you to decide on this.
All the best!!!