Yea I think you need to find a cycling coach instead of a fitness insructor. The instructor could probably help in the gym to make sure you do the exercises correctly but the coach would know more about cycling specific stuff.
As for the big ring stuff, check out your cadence. I don't know what your goal for your age is and there is some mystique in the whole spinning thing anyway...
I'm 42 and I'm now into my end-of-season program. This is a home-made program but it has been working for my high-speed-high-distance-non-race riding.
My off-season consists of keeping my 65+mile/100+k Saturday & Sunday rides with a speed around 24mph/38kph... An occasional 100mile/160k ride is thrown in to build endurance... Some are hill climbing some are mountain passes.
However my weekday rides which are up to 30mph/48kph for 25miles/40k swtich to
25miles/40k (same distance) but the speed drops to a MAX SPEED of 20mph/32kph.
During the next 5 months I will stay in this mode (I time it with Daylight Savings Time) <The Saturday and Sunday programs don't change... typically 3 weekends of 100k/60+ miles followed by a 4th week of 160k/100+ miles>
While I am doing the slow rides I work on bringing up my cadence, watch my legs, check position on saddle and drops, make sure I'm turning circles not squares
My goal is to build my cadence to be easy to maintain at 105rpms. I will work on some rides or on parts of these rides to hit and hold 115rpms for at least 2 miles/3k. Usually I can sustain 110rpms for quite some time after a few months of practice.
So when I start the season is that I can hold a 105rpm cadence without trying, and as I crank through the season I see this slowly drop to around 99-101.
After doing my 200K/130mile, 165 mile and my 300k/189mile rides my cadence tends to drop. And toward the end of the season my cadence is in the mid 90s. So now the season is over and I'm working on getting my cadence up again. After 3 weeks I can already feel my cadence going up... Can't wait until April!