I have two cocker spaniels. One is 7 and the other is 2. They have got on with each other from day one. They play and sleep together and there is no aggression. The older dog is clearly top dog but very amiable. In the last 2 weeks he has started to push the younger one off his food. No growling and no nastiness just shoves him out of the way. He has never ever done this before and we often look after our daughter's dog and they eat well together. I wonder why this behaviour has suddenly started. Nothing has changed in the household or in their routine.
Your (first) dog is just taking the natural alpha role.
Alpha dogs (or dogs who have alpha behavior) can be identified by some actions, one of them being 'dominant' on the food.
While assuming the alpha role yourself (a point many dog owners neglect or are unaware of) might not solve the problem regarding the interaction with other dogs, it could help you understand how it works. Take a look here: Is your dog dominant. There is much, much more you can find online.
Now to your specific problem, you could train your dog not to steal from the other. It's my recommendation, and I am by no means a specialist, but here is what I would do:
Leash the first dog so he can't reach the second one's plate (witch has food in it). Do it without the second dog around at first. Praise the first dog with food when he stops reaching for the plate. Do it until he gets that not going for the food is the way to get it. Require of him increasing time intervals without reaching for the plate before praising him. You can touch the plate or move it a bit to 'tempt' him, still praising when he doesn't reach for it.
After a few goes at that, feed the second dog on the same condition. When the first dog stop reaching for the second dog's plate, praise him. Feed him AFTER on his plate.
I think this could train away the stealing, and ensure you have a dominant role.