In general, Arya Samaj marriages are very simple to execute and the rituals are straight. It is a choice and wiling preference for couples where one person belongs to Buddhism, Jainism or Sikh religion.
Though, Arya Samaj marriage certificate is not a valid document fo marriage in International Law, it's validity is totally different here in Indian Law.
As per the situation you're dealing with, I would like to add on something. Basically, Arya Samaj marriage is just like Hindu marriage, where the marriage takes place around the fire.
Therefore, it is Legally Recognised in India as per Indian Laws.
For more reference you may to proceed to take a glance at the Arya Samaj Marriage Validation Act of 1937, which has been provided under the Hindu Marriage Act (HMA), 1955.
Since it's a legal marriage here in India, you and your wife have rights to live together and if anyone is creating problem then you may proceed to file/register a complaint to your local police station.
The police will then take care of the matter at a base level. If any issue still persists then you are eligible to file a complaint within a Family Court which has competent jurisdiction over the matter.
Thank You so much. Since only two months passed of our marrige. Girl living with her family in other state and I'm living in other state. In which state I can file complain? Any state related to me Or her? Or in her state where she is living with her family currently?
A marriage through Arya Samaj Mandir can be carried out when either the bride or the groom is Hindu and the other is belonging to Jain, Buddhist, or Sikh religion. The marriage takes place according to the Hindu traditions and is legally recognized. These types of marriages are valid and legal as per the Arya Samaj Marriage Validation Act of 1937 that is provided under the Hindu Marriage Act, 1955. Therefore, the marriage certificate holds value in India. In the event of any disturbance in the peaceful life of the aggrieved party, they can approach the police authority concerned.