Windows Docker in swarm with Linux nodes connection issue
I think Windows Server 2016 needs at least 17.09 Docker EE to support overlay networking and VIP's. I recommend updating it.

I was wrong, the latest version is indeed 17.06.2-ee-6 and should support overlay and VIP.

Second, ping isn't a good test, as it may not be available on the VIP or container IP depending on the setup (Docker has changed over time if the VIP does or does not respond to ping). I recommend using something that tests the Exposed container port, like curl. For testing you can just use something like bretfisher/netshoot which has common utilities like that installed.

Third, you could be resolving Swarm services on the network using the service name, not the internal hostname of containers. Depending on which network endpoint mode you use (VIP or DNSRR) in the service, this will resolve the correct VIP or the correct container IP for other containers on the same Docker network.

Also, you want a minimum of 3 manager nodes to follow raft consensus rules in a Swarm. 2 managers actually makes it less fault-tolerant then 1 manager.