When waters drains in our kitchen sink, dirty water rises and fills the bathtub and toilet in one of our bathrooms. Does anyone know why this would happen and the least expensive way we could go about fixing it? Any info would be extremely helpful.

You have a blockage in the drain system after the tub and toilet. You will need to have a plumber come and clean out the piping. You may try and use a plunger on the toilet. Hope no one flushed sanitary products down, they are very problematic if trapped.

Pretty much agree with ma0641 but you can skip the plunger, the clog is down stream not in the toilet. Got a clean out anywhere, maybe in the basement? When I plumb kitchem sink I install a clean out on the line coming out of the wall so take a look there first

That was just a long shot! Brian

As suggested above, it is clog in main waste pipe. Have it cleaned.