I agree with your mother, the nitrates really are not healthy. But I understand what you mean, by giving her hot dogs is better than nothing. Other moms have mentioned looking for a natural or organic brand. That would be your best bet I think. Since she is growing so quickly at this age, everything she eats is absorbed like a sponge and used to help her grow. You really don't want her growing up full of preservatives and chemicals, etc.
Also remember, she is at the age where she can learn that if she refuses to eat what she is given, she knows she can get a hot dog. She is NOT trying to manipulate you in a negative way, but she is learning the cause and effect here. All she has to do is refuse the healthy meat, veggies, etc, and bam, there's a hot dog. (I know it's probably not that straight forward, as I'm sure you try really hard to get her to eat other things, but you know what I mean). So, my point is, if there aren't even any hot dogs in the house, it won't be an option and she will learn that too, eventually. She will forget about them after a while, and move on to other foods. It can take up to 12 times of introducing a new food for a child to get used to it.
I have worked in child care for a number of years, mostly with toddlers. At lunch time, there is no refusing foods, they all eat what they are given because they know that there is no other option. At home, however, they may be pickier eaters because they know they will get something else if they don't want what is on their plate. I have seen this consistently among all the classes I have taught, they just eat what's on their plate. None of them ever ask for something else because they know it's not an option.
I know some parents give their children the meal, and if they don't want it, then they don't get any snacks or substitutes. But the next time they are hungry, they get that same meal again. (Unless it's from dinner to breakfast, then you would fix a fresh breakfast). I know you are worried about her gaining weight, but now is the time to set the standards you want to have and it will go a long way by starting them early-- especially if you want to avoid becoming a short-order cook for you family.
Here are a couple of good articles:
http://www.askdrsears.com/html/3/T030800.asp "Feeding Toddlers: 17 Tips for Pleasing the Picky Eater" It has good ideas for introducing new, healthy foods to toddlers.
and
http://www.askdrsears.com/html/4/T040200.asp "ABC's of Teaching Nutrition to Kids" I thought this one was especially good because it teaches parents how to make learning about healthy food fun for kids. It talks about how to educate kids so that they make healthy choices on their own later on and so they know which kinds of food are healthy and why. The only thing I didn't agree with was that he suggested rewards, but everything else was pretty good advice. The article talks about referring to "grow" foods for kids. At her age, you could start by letting her hold fruits and veggies in the shopping cart and talking about the colors, etc. She can wash them in the sink and let her watch you prepare them. Anything she can do to become familiar with different foods and feel a part of the cooking process will help.
Best wishes!
C. G.