I'll tell you what worked for me when I was in your situation (about 8 years ago). Also, I have to tell you that for me it was important not only how much my kids ate, but what they ate, as I am a strong believer that a very important aspect of good health is what we eat. I did not want to give in to just serving what I knew my kids were going to eat without my coercing them.
My husband and I would cook freezable dishes on the weekend. If something we wanted to eat could not be frozen I would do the prep work first thing in the morning (because I was not tired again and the kids had just had breakfast) Do this when it works for you. Also, my husband and I both love to cook and eat, but we gave up time-consuming meals during that period of our lives. That doesn't mean that you give up on taste and nutrition. There are lots of things that you can fix in a jiffy. At each meal there was always at least one thing that I knew my kids liked. When I served them dinner, in their plates there would be some protein, some veggies & some grains- sometimes these would be combined if I served, for example, beef barley soup with peas and carrots (there was always bread on the table). The portions of each thing were always small, even for their age. My one rule that I stuck to it even on the hardest days was that to have seconds of anything you first had to eat what was on your plate. Since first servings were always small, that was something that my kids could do. Since at each meal there was always something they liked I NEVER had to bring anything else to the table if they were not liking what they were eating. My kids are older now (three kids ages 7 to 12), and they are all adventurous and healthy eaters.
If you decide to follow this, you may want to start at lunch time when the kids are less cranky. It will be hardest with your 3 y.o. but don't give up too easily.
Good luck!