I have a Whirlpool built top load washer with an agitator. It's the same design as your 20 year old Kenmore, as they were built in the same factory. However, I have sold and handled service calls for the ones like your new one. They do take longer to complete the cycle. But it should spin even more water out than your old one, therefore saving on drying time. Have you called Whirlpool to have them take a look at it? I believe there is a problem that can be fixed. As to needing an extra rinse, that may simply be solved by cutting way back on detergent. They use so little water that you don't need much detergent.
One other thought: Are you using HE detergent? Using regular can cause the pump to suds lock, making it unable to pump the water efficiently. Even if you are using a smaller amount than usual. It is so important that the manufacturer may void the warranty if you don't use HE. If that's the case, have her run a quick load with 1/2 gallon distilled vinegar and start over using HE detergent.
15 years in appliance sales and service