My crystal ball is broken today, so I cannot tell neither the model of your karaoke, nor the model of your mics. And I am positive the manuals for these devices do hold some info on the subject.
karaoke is a wired 10 yr old vocopro bravo its been overhauled, headphones are sony wireless MDR Rf985 with transmitter TMR RF985R, wireless mic is technica DR T260, reciever is ATW R700 it's hooked up from extra input on phones transmitter to phone jack on bravo singing in mic lowers the bravos music down and sounds tinny so I took phones off and switched bravo to internal speakers it works great but I live in apt. and need to keep sound down and use phones bravo works great with wired phones and wireless mic, I want to do away with wires, also manuals have no info on this matter, otherwise mic works good with wired phones I will greatly appreciate any and all your help you can give, Thank You.
Forget the headphones / receivers for the moment. You're entering too much "noise" in the roubleshooting.
If I get your problem correctly - when you use wireless mics, music volume goes down. What about when using wired mics? Do the music goes down only when you sing?
Yes even with wired mics but when I switch karaoke to internal speakers without headphones it sounds great and no problem with wired headphones using either mic, the only problem is with wireless non bluetooth headphones