I believe, log-shipping would not work in your case (AG1 ot AG2), due to following reasons.
- Database cannot be restored while it's already part of AG/Mirroring
- Basically, Log-shipping does backups on primary replica, and restores on secondary replica with defined interval time
Log-Shipping would be good choice when Secondary replica in Log shipping topology is standalone and same version as primary SQL Instance. i.e. Your Data-center-1 AG act as primary replica and Standalone Instance at Data-center-2 act as secondary replica.
While you implementing Log-shipping for a Database that is already part of AG, you need to ensure that the Backup preference cannot be set to secondary within AG as the log-shipping cannot work with secondary backup copies from AG. In your case AG of Data-center-1.
Since you already have Availability Groups in-place with SQL 2016 in two sub-nets, distributed AG might be correct solution.
You may follow these reference in either case:
Distributed Availability Groups
Log-shipping from AG Database