Just did this. Mount has a square top that fits into recess in engine side mount. That part is rusted in place. Try an air hammer on engine side mount to break up the rust bond.

 

This may help:
http://www.siennachat.com/forum/66-problems-maintenance-repair/8093-motor-mounts.html

 

I had the same issue as EthanSienna. The driver side engine mount was replaced with no issue. However, the passenger side, I had tried 3 times with no success (Yes, I had to replace my control arm 4 times* within a year on the passenger side). The engine mount on the RH was not stuck per se, but would not clear the subframe. If I jack/lift the engine too high under the oil pan, the whole vehicle would come off the jack stand....presenting a danger. And yes, I've remove the top engine mount (by power steering fluid) and loosen the front engine mount (by radiator). I've even loosen the sub frame bolts but it made no difference as the subframe did not separate from the engine.

The last mechanic I used decided to cut the RH engine mount and just replace it with a new one. That was the only way the mechanic was able to replace the passenger side lower control arm. If anyone has an idea how to get that RH engine mount off (without cutting it), I would love to know. Thanks.

*Lower control arms replaced:
1) BecksArnley Lower control arm - lasted less than one month as rubber bushing cracked and ripped. Don't get aftermarket lower control arm
2) Problem Solving (PSB) Polyurethane Bushings - Lasted about 2 months and it ripped on the top part and eventually broke into pieces.
3) Problem Solving (PSB) Polyurethane Bushings - PSB sent a new one for free. Installed and again lasted about 2 months and it ripped on the top part.
4) Toyota OEM Lower Control Arm - Just installed last week before the PSB bushings fall completely apart. We will see how it holds up.

 

So , how is the OEM holding up?