Can I have two ReadyNas 316 (or another model) systems auto back up to one another?

It is possible.  You can use replicate to back up to the system at your house.  

There are a couple of options to back up to the cloud.  What make sense there depends on what cloud service you are talking about.  I use crashplan on my pro-6 - that needs to be manually installed with ssh and requires some linux knowledge.  Though you can alternatively install crashplan on a windows-10 system, and mount the NAS volume as a network drive - backing up the NAS through the windows 10 system.

Amazon Cloud sync is in beta, I am not sure if it is ready to do what you want yet.  

You could also use Egnyte, you'd need to contact them for pricing.  But it looks like you'd get 10 TB of cloud storage with a single-employee license for $15 per month.

If your intent is that the contents of the two NASes will be the exactly same, then Replicate is not your answer.  Though they call it "Replicate", it doesn't truly replicate; it's a backup and versioning system. Not that that's "bad", it's just not true replication.  The backup files do not go into the same directory structure on the backup as on the source.  If your primary system dies, you can buy a new one and restore from your backup.  But you can't rename the backup machine and have it take over from the primary.

And if you will be adding and deleting or changing files on both NASes, I don't think there's a good solution, either.  If you use RSync and set it to delete files on the target that have been deleted on the source, it's also going to delete any files you added to the target but not the source.  Likewise, if you delete files from the target or modify them there, it's going to put them back from the source.  So, you can only have one primary and one backup system, not a two-way cloning.  If you use something other than RSync, it won't delete files on the target that have been deleted on the source. 

I tried to figure out a way to use a combination of methods to produce cloning when files are being changed on both systems, and could't do it.  Robocopy via a Windows computer or some other third party sync method was the only way I could see to do it.