Addressing my Sangean DT400 radio grabbing two FM stations at the same time, Gary writes:
This is related to FM capture effect. With FM, you're only supposed to hear the stronger of two signals on the same frequency. This is in contrast to AM, where many signals can be heard at the same time on the same frequency.
There is a limit to the FM capture effect, and it's measured by the capture ratio, which is the number of dB that one signal must be stronger than the other for only the stronger signal to be heard. If the signals are closer in strength than the capture ratio of the receiver in use, then both will be heard. It sounds like this is what's happening in your case, and it may not be easy to resolve with a different inexpensive portable radio.
If you move location slightly, this will probably change the strength of the two signals enough for one or the other to become dominant.