How should I set parameters of color profile to change only yellow color output (right now I've got #FFFF00 displayed as #B4B400). Other colors must be left untouched. So I cannot just move Red and Green curves as it will break other colors. Is it possible?
Yellow is not a native color of the monitor. The screen is composed of red, green and blue sub-pixels. If red, green and blue all look fine, then something else is going on with the yellow. There is a good possibility that this is a physical limitation of the screen's color gamut, since you said that full red and full green look the same, but full red and full green at the same time look different. There may also be some kind of display optimizer in the driver that is causing the blue color to be boosted.
I would probably start by making sure that there are no "intelligent" color corrections being applied and then try to use a colorometer to create calibrated ICC profiles that will control the response curves for red, green and blue values. If things still don't match, it is probably a gamut issue that the screen simply can not display as well.
Sometimes even when the same color profiling software is used on 2 different displays, the results won't visually match. One reason for this is the white point aim for profile vs two potentially different backlights in the displays. Some Laptop displays are using TFT, and some are using LED, OLED and other various flavors of the above.
The rub comes in when we tell the software to figure out what's "closest" to the actual white point aim for the profile during the profiling process. Since the spectral outputs of these two displays are different, they can easily end up at different "closest" white point value in XYZ compared to the aim values for D50.
So the solution for this in your case is to aim for a different white point after you see the software has failed to choose the correct one. Then just remember which one you chose.