fixing a loose 12 volt socket

I have a 12-volt thermoelectric cooler plugged into my vehicle. The problem is that the socket in my vehicle is loose and I have the hardest time keeping the cooler running as I'm bouncing down the road.

One solution I've come up with is that I'd like to split the 12-volt socket in two (a Y). On one end if the original socket and at the other a firmer quick-disconnect type plug. I'd do the same to the wiring for my cooler, except it would have male parts.

Has anyone ever done something like this? Exactly which type of plugs/connectors should I buy?

Depending on cooler draw (usually Peltier modules range from 4A to 8A) and circuit fusing, it is ok to parallel another cig socket though I'd be using the newer Euro "Merit" types - not the traditional older & larger cig sockets as they are prone to failure and fire.

Same with any interconnect wiring - the Euro cig sockets and plus - with the socket (female) always on the battery side (obviously).


FYI:
I'd power direct from the battery via a fuse - with a relay if I wanted it to be switchable (ie, with IGN, or ACC, or alternator charging, or with low-voltage cut-out, or manually switched).
And I'd probably use Anderson connectors - probably the 50A.

Though over-rated for your application, the Anderson 50A connectors are common and relatively cheap as a DC connector, but require soldering or (specialised) crimping.
And though not designed nor intended to break a powered connection (despite what many think and say!!), a 50A Anderson breaking a 4A-8A Peltier cooler should not be a major issue.
Smaller Andersons are available, but they get fiddly...