How to connect 2 laptops to 1 monitor????

I need some technical help. I'm wanting to connect my work laptop and my personal laptop to one monitor so that I can switch back and forth easily throughout the day without having to constantly plug and unplug a cable. Right now the work laptop (Dell Latitude) is hooked to a Thunderbolt dock and connects to two monitors. I am able to connect my personal laptop (Lenovo IdeaPad 3) up using a hdmi cable to one of the monitors and I'm able to access my personal info. on one monitor while the work info is still showing on the other monitor. I can either unplug a displayport cord from the dock and that leaves my personal laptop up on the monitor. Or I can leave the displayport cord plugged up and when I want to swtich to my personal laptop i just unplug and plug the hdmi cable back into my personal laptop. I want to be able to have the work and personal laptop attached to one monitor and be able to hit one button or switch to go back and forth but the issue seems to be the second monitor that the work laptop is connected to as well. I would love to be able to connect my stuff so that the work info stays up on one monitor but on the other monitor be able to hit a button or switch to switch back and forth between the two. I can do away with the second monitor if needed.

I have searched online and I read about kvm switches and hdmi docks. I'm just not sure what I need. Please help!