How to pull & run docker image on remote server through jenkins pipeline

I have 2 aws ubuntu instance: 1st-server and 2nd-server.

Below is my jenkins pipeline script which create docker image and runs container on 1st-server and push the image to docker hub repo. That's working fine.

I want to pull image and deploy it on 2nd-server.

When I do ssh for 2nd server through below pipeline script but it logins to 1st-server, even if ssh credential ('my-ssh-key') are of 2nd-server. I'm confused how it logging to 1st-server and I checked with touch commands so the file is creating on 1st-server.

pipeline {
  environment {
    registry = "docker-user/docker-repo"
    registryCredential = 'docker-cred'
    dockerImage = ''
  }
  agent any
  stages {
    stage('Cloning Git') {
      steps {
        git url: 'https://github.com/git-user/jenkins-flask-tutorial.git/'
      }
    }
    stage('Building image') {
      steps{
        script {
          sh "sudo docker build -t flask-app-one ."
          sh "sudo docker run -p 5000:5000 --name flask-app-one -d flask-app-one "
          sh "docker tag flask-app-one:latest docker-user/myrepo:flask-app-push-test"
        }
      }
    }
    stage('Push Image') {
      steps{
        script {
          docker.withRegistry( '', registryCredential ) {
          sh "docker push docker-user/docker-repo:flask-app-push-test"
          sshagent(['my-ssh-key']) {
            sh 'ssh -o StrictHostKeyChecking=no ubuntu@2ndserver && cd /home/ubuntu/ && sudo touch test-file && docker pull docker-user/docker-repo:flask-app-push-test'
          }
         } 
        }
      }
    }

My question is, how to login to 2nd server and pull the docker image on 2nd server via through jenkins pipeline script? Help me out where I'm doing wrong.