My DD is fit and healthy. She has a huge appetite and is showing a bit of a tummy due to this. I am looking for ways to manage it. She (as I am sure other kids) would eat 'rubbish' all day. It is very hard work trying to make her see what is healthy and what isn't. I am sure she will get there as we set a good example with what we eat at home.
DD2 is very thin, so I do think it has to do with genes also. She is being brought up the same - same attitude to food and activity. She just never finishes a meal and we have to try and make her eat (otherwise DD1 will hoover her plate!).
So you are force feeding one kid to stop the other eating all her food too.
Thats a good healthy thing to do, rather than let children stop eating when they are full... and to let the eating habits of one child have a direct influence on the other. 
Do you actively tell your DD1 she's a bit bigger than you would like? And if you do, do you do it in front of DD2? Have you stopped to think how this might effect both girls.
You are looking for ways to manage what the kids eat and to stop them from eating rubbish all day. Well start off by not having rubbish in the house. If you don't have it in the house, they can't eat it. And if they are that young, then they can't easily buy extra food from elsewhere without your knowledge.
What sounds like is happening, is already a slightly unhealthy relationship with food is developing as a household here.
And what also seems to be the case is you can't see how what you do and the way you express it, might be a massive contributor. Sounds like DD2 might be picking up on you saying to DD1, that too much food is bad...