I would keep the routine as it is. Do not let him eat in front of the tv unless it is a special family thing (picnic on the floor or something). We keep food at the table. I try to let my kids do fun things regularly like watch a movie in the evening but we have played and done other things during the day, and I use that time to get dishes done, do laundry, or relax for a bit and catch up with someone. It is okay to have a routine that he WANTS to do, just remind him that dinner is first. Bring him back to the table and reaffirm that television is after the family has dinner. Make sure you are not expecting him to sit at the table too long--that is really hard for them as well, especially if he has already eaten.
He cannot really control himself very well yet, so the tantrum is probably him making sure you know how much he wants to do that. Since you regularly let him watch tv he should know on some level that he will get to. Or you could vary when he watches tv so it is not just after dinner to help him learn that it is a treat and to control himself better.
His eating will be up and down. My kids are eating better when I do not insist they eat if they are not hungry enough to. I try to let them play for a while before breakfast, etc. A little television can truly be a lifesaver, especially with a second little one, so I would be the last person to critize that! :)