The noted component below (R3) has been replaced with the external resistor (rather sloppily, IMHO) and
the replacement has obviously gotten pretty hot. A properly designed circuit would not normally over heat the components. Perhaps the baby monitor's battery is defective?
The replacement would appear to be a fairly low value. My guess is that it's intended to be a current limiter with a value of around 10 ohms (or less)..
As the charger has quit working, my second guess is that the diode (D1) may have also failed (too much current for too long) and its failure is the actual reason the charger quit working.
We also have no idea if the replacement resistor is the correct value.
I'd suggest that you remove the PCB from the case and see if you can give us a picture of the other side of the PCB,
at a slight angle, so we can see if R3's value can be determined.
I should note that a resistor's size is generally a good determinant for assuming its wattage capability. No doubt the replacement resistor is probably a 1 Watt while the original is probably only a 1/4 Watt. It's also likely to be "burnt" looking, which will make it difficult to confirm it's resistance value. For the 1 Watt resistor to also be overheating is a sure sign of other problems.
The only way to determine if D1 is damaged is to test it. Do you know how to do that?