From your post, your points are:
- Whether a union (representatives/office bearers) can enter the office/other premises.
- In the matter of negotiations & settlement/agreement, with whom the management has to interact.
There are no restrictions as to who can form the union(s). Any group of employees can form a union subject to the conditions stipulated in the act. It could be either with affiliations or can be independent as well, no compulsions. Registration has to be obtained from the ALC of the relevant jurisdiction. These registered formations should obtain recognition from the management and can function independently or in unison on matters for the common benefits of employees and/or take up matters concerning the welfare of employees. In order to avoid confusion, the law permits only one recognized union as the single formation duly elected among all the registered unions for the given period. While doing so, they need to discuss with various officials of the management. Though the management is within their prerogative to discuss only with the elected & recognized union, often it couldn't be restricted only to the elected one for obvious reasons, like political/social and/or with a view to maintain rapport with all formations for future developments. You'll have the right to deny entry of unions to those who are not elected/recognized unions, provided you have every tactic in your armory to tackle the situations wrought in a particular moment. As a shrewd HR moderator, you'll know in the course of your tenure whom to receive warmly and whom to avoid for the moment in a way fitting within your constraints.
With regard to settlement & entering into an agreement on issues deliberate, you are duty-bound to sign the settlement only with the elected/recognized union. Sometimes major issues, long-term settlements such as wages, leave, incentive schemes, bonus rationalization of manpower, welfare measures, etc., would call for the consensus of all registered unions, in which case the agreement can be signed by all the registered unions, and involvement of ALC as a tripartite agreement is a welcome strategy of the management. How you'll bring all the registered unions on one platform is the secret of success of any HR team and the wisdom of management.
I can cite, for example, the labor/IR policies of the TATA group for others to emulate. I have not heard of any TATA establishment (having their presence in almost all sectors, worldwide) stalemated with labor troubles in the modern era, Uno-WB project which ultimately shifted to Gujarat notwithstanding.