tomek,
I think maybe your source did not like the load as you theorize. When you parallel amps like this you halve the impedence the source sees and increase current demands. If you have, for example, two 100k inputs, thats still an easy to drive 50k load the source sees. However, if you have, for example, 20k and a 15k input impedences, you would have an impedence well under 10k. That would be a very tough load for most cd players. If you know the input impedence of your amps, that would give you a good idea if the load will be to much for your cd players output stage.
There can be an incompatibility issue elsewhere too, such as the capicitance of the interconnects the source has to overcome. Did you use the same interconnects for both connections?Were the interconnects the same length? When you start adding in two loads with two different impedences, and then two different interconnects that have different capicitance etc; that is hard for a source to deal with. One last thought, did the weight of the splitter and the two interconnects pull down the front of the rca's when both were connected and possibly break contact slightly? I had some trouble with this causing some noise and interferance from a source with flimsy rca's.
I am certainly no expert as to why you have had trouble. But I have had some of the same problems in my system. If you use good splitters, the source rca's are rugged enough to support the extra weight, and you have equipment with high impedence input stages to give your source an easy load to drive; you should not have to much trouble getting this to work.