One bathroom sink in my house has suddenly lost water pressure. If any other faucet is running in the house, it goes down to a trickle. Any suggestions?

Hi All, I hope I give enough information here, if there is more info that you need (or something sounds screwy) just let me know and I will find out. I appreciate any help! We rent the 2nd and 3rd floors of a 2-family home. The owner lives downstairs. The house is about 100 years old and I am told that it has 1/2" plumbing - that number may not be right, but apparently the pipes are smaller in this house than they would be in a more modern house. As you can tell, I don't know anything about plumbing :) Our kitchen (2nd floor) has a sink and a washing machine hooked up to the same drain pipe. The sink is hooked up in a ... standard.. way (underneath), and the washing machine feeds into a vertical pipe that also meets the pipe that the sink drains into. The kitchen does not have a dishwasher but we would like to get a portable model (or honestly I would pay for an installable one). However the owner's plumber said that we shouldn't do it because we have only one 1/2" pipe which handles the sink wastewater, the washing machine wastewater, and the dish washer's wastewater (which if it was a portable, would really be going down the sink, if it matters). He thinks that is too much dirty water/particulate for the 1/2" pipe to handle, and that it would clog every 3-6mo. So here's why I'm posting - I would really like to have a dishwasher. However I don't want to be rude and ask the owner for a "second opinion" about the plumbing. I'm hoping that some of the experts on this board can let me know whether they think the plumber's assessment is correct, and if there is any other way that I could get a dishwasher installed given the current piping situation? Note: if you need me to go measure a pipe to confirm the size, just say the word :thinker: Thanks in advance!