When you setup the second domain controller, did you tell it to join a forest? Or did you mistakenly create a new forest? It sounds like you are using the same domain name, but two different forests? I am going to assume that these are two seperate networks, yes?
You are going to need to do a few things, especially if the domain controllers are hosted behind different WAN connections... I am not 100% positive, but, the following is what I would do... Never had a need to connect multiple networks under one domain over a WAN...
1: Create a VPN between both physical networks, and routing rules on your network routers so that the domain controllers can talk to one another, and so that domain connected devices can talk to either of the controllers. Make sure, 100%, that the Domain Controllers can talk to one another, a simple ping should be enough to see if they are talking.
2: Back up the secondary domain controller, and note all the users, policies, etc.
3: Setup a NEW secondary domain controller, set it up and have it join the primary domain forest. Do not create a new forest. Pretty sure you can just remove the role and reinstall it and create a new setup.
4: Make sure replication is working by checking the secondary domain controllers users, and GPO's to see if it pulled from the primary controller.
5: Once replication starts, you can add users and policies on the primary, if needed you can create separate User/Computer Groups if policies at the two locations are different.
6: Have each network look at either of the Domain Controllers (that's the purpose of having more than one Domain Controller in a Domain), but setup DHCP so that each network is only sending queries to the local DC DNS, this would reduce load on the VPN side.
7: Make 100% sure that no Hostname is used more than once on the entire infrastructure. If you use fileserver.domainXYZ.local on Site One, do not use fileserver.domainXYZ.local on Site Two, otherwise DNS will replicate that between both controllers, and you will run into some strange, annoying, and time consuming headaches.
This should allow users that travel between both sites the ability to log into either site and not get an authentication issue, and to also use work laptops between both sites with out login issues.
Veeam wouldn't be of use for this, this is purely a network, and server configuration issue... If you can't create a VPN between the two networks so that they can communicate with one another, I think your only other option is to use something like Azure Active Directory, but I am unsure on that. If none of those options are viable, use a different domain name for each network, and login to each domain separately when at the specific location. For example, at the first location use yourdomain01.local and at the second location use yourdomain02.local and instruct users with machines that travel between locations on how to log into that specific locations domain.
Note that if you use a VPN to connect the two networks, the link between them needs to be rather decent, and routers at both ends need to be able to support a fair amount of traffic.