Advice needed for shuddering issue

2009 Corolla shudders/vibrates on acceleration

Trying to help my father-in-law figure out his issue with his car.

I just took it for a test drive and it is smooth acceleration until it hits about 25mph(40kph) - 45mph(70kph). Between those speeds, the vibration is the worst. Once it gets into the higher speeds it is still present but not as severe. The vibration stops when foot off the gas at any speeds. Foot back on gas, vibration returns. At around 75mph or 120 kph it practically smooths out again.

It seems to shake the whole car so hard to tell where it is originating from. Also seems to be a bit gutless when getting to highway speeds but maybe that is just because I normally drive a V6 Outlander.

Anyone have any ideas on what we should be checking?