what would be a good supplemental excercise that could be done at the gym that would have good carry over for useful cycling leg strength? maybe leg extensions, hamstring curls, calf raises, etc.....?

basic squats, deadlifts, single leg work, lots of core work.

generally coaches say to avoid the machines that only work one muscle group, such as leg extensions and ham curls.

there's lots of debate about whether gym time is more productive than bike time, for bike fitness; but I'm a fan of gym time because I'm older and I need overall strength - cycling all the time is bad for you in a lot of ways.

stair machine. wear a pack and put weight in it if you need more of a challenge.

IMO I do Yoga https://www.facebook.com/EkhartYoga

Hip opening sequences. it's is low impact
If i had a swimming pool i would be running in the shallow end

What is the use of tearing you body apart with weights when gravity and your own body will provide.

With weights you will add lots of muscle which is added weight. you want to stretch muscles and lean them to keep weight down.

Yes, yoga is great, I do it too. Yes, running in the pool is lower impact than other kinds of running. No, weight training does not "tear your body apart" and no, weight training does not automatically mean that you get big muscles, and no, stretching muscles does not keep your weight down.

+1 on hip opening sequences.

Walking lunges with light dumbbells in each hand... low weight, high rep. Burns like a sun of a gun and really helps build explosive power.

all these gyms workout help, but the best way to increase endurance, speed, and stamina and putting in some seat time and just riding it out. I've asked many cyclists who have been doing this for years and that's the best advice I was given. Before and after my rides I try to do some yoga to stretch my muscles and a bit of leg work outs just to hopefully make a little difference on my next ride