The modulation from the 555 will couple to the transmitter through unwanted paths depending on a few things. First of all, if you have built the circuit on a plug type breadboard (white plastic with the strips with tiny holes for pushing wires into), then you will have lots of parasitic capacitance and this can provide a path for the 555 output to get to your oscillator. You can test this theory by building the 555 oscillator on one board and building the HF oscillator stage on a different board and then connecting them together with an AF wire and a ground wire.
The next path is through the DC power supply. The older 555 circuit (the one that is not made of CMOS) is infamous for being noisy. Since it draws current from the power supply in sharp spikes, it is hard to provide enough bypass capacitance to keep it quiet. Sometimes a little bit of series resistance is needed in the Vcc line to help the bypass capacitor do its filtering job at higher frequencies. One way to test the idea that there is 555 noise getting through the Vcc line to the modulator is to use a separate battery for each stage, to completely isolate their power supplies. If this makes the problem go away, then the unwanted coupling is through the common power supply. Usually, when we use a more modern CMOS version of 555, this problem is much less of an issue, since the CMOS version requires much less current.
The 555 signal can be coupling to the oscillator through the ground line as well, for roughly the same reasons as it might couple through the Vcc line. The ground currents flowing from the 555 can be rich with spikes, and this current flowing also through the ground side of the HF oscillator can cause small voltage spikes to affect the oscillator. Isolating the two stages and feeding power in a star or hub-and-spokes grounding method may help. You have to make sure that the ground current from the 555 does not flow through the HF oscillator stage.
It would be helpful to see your circuit. Can you post a close-up photo showing exactly what your circuit looks like?
For the lowpass filter, just try a single order type (simple series R shunt C) for now and see if the results are good enough. Be aggressive with your choice of cutoff frequency, slow the edges down.
You wrote 50 mA. Did you mean to say 50 mV? And is this peak-to-peak or RMS?