Exercises to strengthen Core and Lats

Do you have any ideas to burn visceral fat, Gary?

I have a bit of a spare tire and get called tubby! haha

any burner ideas?
from my understanding you need to make your body catabolic to remove any substantial fat. Adding cardio can help to shed the kilos but from what you have shared any more exercise would be overkill. I think yor inability to lose weight would stem from diet issues. Too many transfats, saturated fats or unnecessary carbs could be to blame.

Transfats can't be digested properly as it is so you should steer clear of those. Saturated fats should be minimised and as for carbs, removing all refined sugar will go along way. Other things like replacing white bread for wheat and the like will also help you out here.
Your back isn't that important to work out for rowing. It's your arms and legs that you should be focusing on most. Although, from my experience, doing squats really helped with my back region.
There's a good chance you're sore because you may not be warming up before a workout. Good workouts for your lats and core would be doing plenty of deadlifts as well as squats. Don't go too heavy but include them in your workout and your core and lat strength will increase considerably.
Your lower back isn't supposed to hurt - are you sure you are not over straining or using the wrong technique?

For core, I would suggest elbow planking or side planking. Sit ups work mostly on the abs but not the core. It's different.
For your arm muscles, dead lifts are a must, and like Wonderz said, pullups are great if you can do them.

However, the best training would be working on your calves, since that is the main muscle for rowing. Try doing squats and lunges - I guarantee that if you do them properly and consistently you will see an improvement in your rowing times.

Good luck in your aspiration to be a competitor!
The best exercises for strengthening your lats are pull ups and rope climbing. These exercises have worked well for me. To strengthen your core I would use planks and exercises like squats, lunges, deadlift etc with no weightlifting belt.