It looks like there are no tees made that is 1/4" all around for what is needed. You could call Brass craft if such one is made. This is what is needed in 1/4 all around.
This BrassCraft 3/8 in. x 3/8 in. x 1/4 in. Compression x Compression T-Fitting adds another outlet to a water supply valve allowing 2 supply lines to be
www.brasscraft.com
Where the coffee maker is, is the kitchen sink on the same counter? If yes you can change the cold water stop valve with a dual shut off valve.
To be able to tee off the ice maker wall box is possible, however it may be beyond your skill set. Between the floor and ice box there should be about 12". Remove the trim ring of the wall box and cutout drywall below it. It should be possible to tee off the supply line and install a second wall box.
Another way is using a short length of 1/4" copper tubing but it must be formed to a curve using a spring bender so it hugs the wall. Remove the braided line install the copper tubing using a compression fitting. At the other end install a 1/4"x1/4"x1/4" tee with compression fitting. One end to the tubing with a compression fitting, the braid line is just thread on to the fitting. The water line to the coffee maker would be threaded on or use a compression fitting with a sleeve inserted and compression nut.
If this is important you may just have to hire someone.