Open tab on Terminator as root on user's Terminal via SSH

I'm using Ubuntu 22.04 and I have a terminator process that runs as my local user on boot, while I also have SSH access to the machine. I want to open a tab on the terminator window running under my username via SSH, and run a script as root in the tab that opens without needing to enter the password on the local machine. Is there any way to do this easily? To clarify, I'd like to have a script where I enter the password via the SSH session, check if it's correct, and then launch the script (or multiple scripts) in separate tabs as my user (so they open in the terminator window my user is running), but run the scripts mentioned in the SSH script using sudo with the password provided via SSH.