I provide a simple example for NAT/PAT and PAT as a suggestion how you might implement this using those two hosts.
Private Side Public side
Host 1.1.1.2 -> {NAT Gateway 1.1.1.1 <-> NAT Gateway 20.2.1.1} ------------>Host 20.2.1.3
SB1 -> Source 1.1.1.2 -> Dest 20.2.1.3 -> Gateway 1.1.1.1
SB2 -> Source 20.2.1.3 -> Dest 20.2.1.1 -> Gateway 20.2.1.1
NAT
Private Side Public Side
Host 1.1.1.2 -> {NAT Gateway 1.1.1.1 <-> NAT Gateway 20.2.1.1} -> Host 20.2.1.2------------>Host 20.2.1.3
SB2 -> Source 20.2.1.3 -> Dest 20.2.1.2 -> Gateway 20.2.1.1