As a (now-retired) broadcast engineer, I grew to hate the LM-386. It always seemed to me to be difficult to control and to be prone to oscillation.
My own solution was to switch to another chip for audio amps. My own choice was the TDA2822. It’s inexpensive and easily available from Mouser, Digikey and others. It’s a dual amp, which is handy for stereo, but I use it in bridge mode even when I design mono amps. My choice is the SOIC-8 package, which is large enough to be easy to use, but also saves pc board space over the DIP-8 that’s usually used on LM-386 chips.
My general tips are to carefully bypass the power supply for whatever chip you use. I’ve often used 4.7 ohms or so in the supply line, and tried to bypass it close to the chip with an electrolytic, a .1 uF and a 20-100 pf chip capacitor.
But the MOST important tip for taming IC audio amps is to connect a small capacitor (I’ve usually used 33 pf chip caps) between the inverting and non-inverting inputs. It tamed lots of otherwise-troublesome amps for me.