Actually I did not make the assumption you knew what you were doing - I suggested that you talk with her and have her set up an appointment with a trainer.
You are also simplifying what you need to do with the equipment - the machines in a typical gym are not all that simple to use. And just observing someone (that may even be using the equipment incorrectly) will not teach you the correct way to use it; which weight would be appropriate for your abilities (no it is not so simple of - oh it is too heavy put lighter weight) you need to know how many reps are most effective, which weight is best, how often to use it, the right posture, etc. You can get hurt or injured if you do not properly use this equipment and some you do need a spotter with you.
I'm just there to drop a few lbs. So for me, working out on the treadmill is 100% fine with me. It is giving me everything I am looking for.
Sorry but this sounds very selfish - and most of what you are saying does. Great it works for you but at least from your comments, it sounds as if great it works for me - too bad it doesn't work for you - leave me alone and deal with it.
A caring husband would at least make some suggestions - I see no reason that you need to do the same routine she does but at least listen to her and be open - I am thinking this is sort of your alone time - but she is seeing it differently. Maybe explain to her - I love her but at the gym I like to work out alone with my earbuds in and just go on the treadmill. It is my down time and stress reliever. Maybe we could go out to dinner and be a couple there or is there some other way we can do something together.
The thing is - she is not getting what she needs, but you are. As a couple there should be a way to work it out so you both get what you need.