I currently have a nikon d3100, which i know isnt the best but im just beggining.
Equipment is only one part of taking great photos, and your D3100 is fine for getting started. Learning to control the various parameters (shutter speed, aperture, ISO, composition, lighting) to create the image you want is far more important than having the most up-to-date camera.
My question is what am i missing in my lens family in order to reach my photography goals?
Nothing. I think you've got a fine collection already. In fact, for your stated goals ("newborn, family events, birthdays") you probably don't need the 55-200mm zoom.
I'd suggest saving your lens money for now and instead getting a better handle on what you already have. Sit down and pick out the photos that you've taken already and for each one ask yourself:
If you can do that honestly and objectively for a few dozen photos, you might start to notice a pattern in the things that you like, or the things that you'd like to improve, or both. That's valuable information that can help you improve your photography on your own. If you have friends who are good photographers, you might show them the same images and see what they like and/or would do differently.
Another thing you can do is to look for other people's photos that appeal to you. Pinterest is a great tool for collecting images from sources like Flickr, photo blogs, etc. Look critically at the photos you like and try to figure out how they were produced. Sites like Flickr often help here by providing info like shutter speed, aperture, and focal length, but make sure you also look at lighting, composition, color, and depth of field. Pick some favorites and try to take your own photos in the same style.
I dont know if my next lens should be a 35mm f1.8.or say 18-50mm f2.8...or even both?
If you don't know which of those lenses to choose, it might be because you don't need either right now. When the time comes that you need (or just want) a 35mm f/1.8 or an upgrade to your 18-55mm kit lens, you'll know it. Before that point, having those lenses in your bag might lead to some nice shots, but it'll be more accidental than intentional. Your goal should be to get to photos that are 100% intentional.
I also am on a budget i will not spend more than 275.
That's just another reason to wait. When it comes to lenses, more is not better, but better is more. A bag full of cheap lenses won't make you a better photographer. A bag full of expensive lenses won't make you a better photographer, either, but as you become a better photographer you'll be better able to take advantage of a really good lens.