Just stop doing it. What you serve is what you serve, period. You can add a side dish of a favorite, have them wait to eat that part until other things on their plate have been tried, but they are to eat what you serve or they can get down. I am hard nosed on this rule. I allow my kids a few things they just don't like, they did try them a few times and we just don't have those things. Kids have things they don't like and I totally am okay with that.
However, if they do not want to eat what you give them or even try them, that is fine, nothing later or you can reheat what you made earlier and they can eat that! A few nights of you being hard core about this it will help. Let them just be. It is a power struggle now. If they don't mind being hungry neither should you. Of course as a parent your natural instinct is never to want your child to be hungry but if you serve something and they refuse then that is that.
Your one year old needs more calories and nutrition still, sounds like your four year old has set a poor example. That happens a lot when the older one is picky. Maybe empower the four year old to be a great big brother and show how cool it is to try new things to his little brother. I would still make sure the 13 month old gets the calories he needs somehow. Make it fun, whomever can try the most new things in a week wins! :) You have enabled this too if all you have given them is chicken nuggets.
You can try charts too, so for every night they are willing to eat half of what you serve a smiley, no smiley just for one bite! But if they eat all their dinner two smileys, after 10 smileys they get to pick dessert that night.
Dessert I hear isn't to used as a negotiating tool, but it is a lifesaver in my house. If they want dessert, they are to eat 80% of their meal. I don't over do at dessert, pudding, two cookies, a scoup of ice cream but is a strong motivator for my kids. They both know they do not have to eat and some nights they really just don't want to eat what I serve and deal with the consequences. They will not starve themselves. I do not like the however old you are bite rule as one bite of dinner is not doing it for a one year old. You should be willing to put up a list of things they have tried, give them both five things they just do not like, BUT THEY HAVE HAD TO TRY THEM, then tell them that is fine on those five or six things. Otherwise they have to eat what you give them. Have them help in making dinner too as that sometimes excites them into eating what they helped with.
Make sure too your boys have not snacked within two hours of dinnertime. SO they come to the table hungry and much more willing to try something new.
Do not cater to them or you will be set up for a very long time of picky eating! I have a friend that has a four year old that she caters to and it is a daily struggle because she caves in all the time out of fear her daughter will starve!