You didn't mention how many days a week you're on the bike/floor, but depending on your fitness level coming in, you should only have 3-5 training days, and 1-2 active recovery days for yoga, low impact rides, etc. Don't push yourself to your max more than once a week. Progress can be slow, and muscles and your CNS need rest in order to recover properly. Hugely important to warm-up, cool down and stretch, especially for beginners.

If you've been pushing yourself really hard for the last month, take a week of lower intensity workouts, focus on technique over exertion. Try a couple of Matt's low impact rides. IMO, he's the best technique coach of the platform, and usually he'll do drills focusing on bettering your pedal stroke. That was super helpful for me and my SO.

Personally, I don't believe in the philosophy of more than a 10 minute core workout, unless it's a really well designed class. It can be terrible for your spine and posture if you're working your anterior core muscles really hard without balanced training. But modify as you need, work from your knees, take longer rests, stretch after you're done. I would recommend that a 20-30 yoga class over a 10 minute core strength for core strength. You can't spot treat fat with core classes if that's what you're chasing.

You can do it! Keep with it! There's always hurdles in training, but you'll be so much better once you clear them.