3. Use two DisplayPort to HDMI cables to connect the existing dock to the monitors, Use two DVIs to connect the new machine. Switch inputs on the monitor to change between.
I regularly use this option with my computers. It works well and is cheap (assuming you have two keyboards and two mice and potentially have all the needed cables...but even if you need to buy additional cables, they are typically not that expensive). As noted by Kilroy
, most modern monitors will automatically switch to the active signal if you operate by way of turning off and/or disconnecting the computer not being used. If you want to have both computers running, then you will have to push a button (or more) on the monitor to switch to the other computer.
Of course, the biggest potential wrinkle is whether your monitors support multiple inputs and what inputs they support. The vast majority of modern monitors do support multiple inputs and that appears to be the case with your monitors. And it appears your monitors support DVI, VGA (aka D-SUB is how it maybe called in many tech spec descriptions), and HDMI. So, you should be good in this area.
The major downside of this approach is that you will have to operate two keyboards and two mice...one for each computer. This means extra desk space with the extra set of the keyboard and mouse of the computer not being used kind of being in the way sometimes. For my main setup (which has my main computer, a MacBook Pro, as well as my older Windows desktop), I use a wireless keyboard and mouse for the Windows desktop that is stored down on top of the tower inside the cubby in the desktop that holds the tower, but then I don't really use that old Windows desktop any more (the MBP has a wired keyboard and wireless mouse that stay out on the desk all the time since it is the one used 98+% of the time).
All of your other options outlined, as well as Kilroy
's first suggestion, would not have this downside of needing two keyboards and mice...with the possible exception of the two switch option (i.e. #2), but that will depend on the switches. If having the two keyboards and mice is not desirable or even a deal breaker, then which other option you pick would depend on a number of factors...at least in my mind.
For example, will a laptop that will fit the existing dock fits you needs or desires for the new computer? The corollary question is what are your needs/desires for the new computer? For example, do you want to do gaming with it? If so, will a laptop that will fit the dock be capable of playing the games you want to play at the performance level you want? If you cannot find a laptop that fits those needs, then that kind of rules out the option of getting a laptop that will fit the dock and leaves you with either some sort of KVM switch situation or maybe the remote desktop option (all this assuming just using the monitor inputs are not an option).
Deciding between the two switch options will depend on how much you want to spend, whether the two switch option requires using two keyboards and mice, and potentially expected dependability and reliability of the switch(s).
And going with the remote desktop option would be the cheapest, as noted by Kilroy
, but would also depend on how feasible it is (i.e. whether the work laptop is locked down as well as whether routing a video signal through a network connection, in effect, might cause video lack that creates problems for your use...it would depend on your uses and your home setup).