Shadon,

There are lots of girls here who can give you very specific, excellent advice, I'm sure - whereas mine will only ever be general and waffley!

It sounds, from your post, that you might be over-training if you're feeling so tired and craving rest. Rest should be a very important part of your training, along with actual exercise. If your body's fatigued, one day's rest will benefit your training more than one (or even two) day's exercise.

Gym/cardio work will improve general fitness and stamina, to some extent, but if you're looking to specifically improve your average speed, then there's no substitute for actually getting in the saddle and putting in the miles.
I used to be a spinning addict, but still found that when it came to keeping up with the pack, even spin classes were second best to getting out and turning the pedals!
There are some advocates who swear that spinning or turbo training can sometimes be even better than the real thing - but personally (and that's all I can judge things on), that was never the case for me. And I gave it my ALL in those spin classes, believe me!

My average speed has increased quite considerably over the past year and the only things I can attribute it to are the fact that I cycle more (commute, events, training, club rides), I ride more hills (great for stamina and strength training) and my training program is more varied. I now mix up my training with easy rides, hard power bursts, sustained stamina rides. I guess, in other words, I now do interval sessions and interval training.
I generally cycle 6 days a week, but have started to appreciate the benefits of that all-important rest day. Not only does it give my tired old legs a break, but it also helps me to refocus and really look forward to getting on the bike again (absence makes the heart grow fonder!).

From your post, it sounds like you ride with a bunch. Are you sure the bunch is the right pace for you in the first place? There's nothing more demotivating than trying to keep up with a group who are just gonna burn you out. Has your performance plateau-ed, or dropped? How do you feel after your rides - is the pace comfortable or do you feel over-stretched?

Do you vary your training? How often do you ride? What is the terrain like?
If the terrain you ride with in a group is quite hilly, but the terrain you train in on your own isn't, that could significantly affect your performance.

Sorry to bombard you with questions, but there are so many different factors involved when it comes to training, there's never one specific answer you can give!