Need advice on fixing washing machine overflow

[Vicky1203]

• older home with 1.5” copper piping
• Laundry ties into kitchen drain
• overflows from washing machine within 10-20 seconds
• Can withstand full pressure from outdoor hose for more than a minute before slowly overflowing. Will drain if allowed at a lower rate.

Have had multiple plumbers out who do not know what issue is. They’ve tried snaking but had trouble getting past the “T” elbow”.

Any advice or insight would be deeply appreciated thank you.