buzzing relay powered by radio power ante

If i turn the ignition on first , I have no problem but if i turn the radio on first the power from radio does not seem to be enough to close relay as relay buzzes.

Is this supposed to work this way?

In your picture, Is your Amp / Power ant lead turning ON the Relays?  Or R U trying to supply Power to Amp / Power Ant lead?

i would leave pin 85 of the first relay as it is, but hook up 87 and 85 of starter kill relay to 12 volts.....

that way p ant activates the relay which then uses 12 volts to energize things.....  keep in mind the p ant out is only about 100 ma.....

It appears U may be getting a low voltage from your Amp/Power Ant Lead.

Two things I can think would cause probs.

a) low volts from the aerial output of the radio or excessive volts drop across the series diode, AS the circuit is drawn I can.t see a need for the diode. If it is needed to isolate from another circuit check its rating. Low cuttent diodes  - aka 1n4148 = 50v iA diode tend to have a comparatively high internal resistance if only handling 100 - 200 mA relay current. Try putting in a dummy load in parallel with the relay to force more diode current or use a schottky diode with a lower internal resistance.

b) is there any interaction caused by the ignition feed to the radio not being active until the ignition is live. Disconnect the relays and see if the radio performance varies with the ignition on or off. Also check if there is a power aerial fitted requiring the ignition to be on to be fully operational causing additional loading on the radio aerial feed wire.