&
no final de um comando coloca o trabalho em segundo plano.
Eu reescreveria meu script
connector.sh
#!/usr/bin/env bash
echo 'date' "Executing $1:$2"
# 1 host, 2 cmd, 3 log
ssh $1 "$2 | tee $3"
adicione o script runner.sh
#!/usr/bin/env bash
connector.sh 127.0.0.1 /sc/db2home/scbinst/bin/reload_scrpt1.sh /var/log.log &
connector.sh 127.0.0.1 /sc/db2home/scbinst/bin/reload_scrpt2.sh /var/log.log &
connector.sh 127.0.0.1 /sc/db2home/scbinst/bin/reload_scrpt3.sh /var/log.log &