Welcome to Guitar Tricks and to the guitar. You may be relieved to know your problem is extremely normal. I teach adult beginners all the time, and many will come to me after a few weeks or months of practice and say something like, "I can't believe how much trouble I used to have with the C chord. Now it sounds just fine!"
I have yet to meet a student who had to go out and get an especially wide necked guitar, but in answer to your question, yes they do exist. For starters, you might try a classical guitar. They have a noticeably wider neck, but also have nylon strings - which will have a different sound than a steel string acoustic.
I have a tutorial for beginners that may be of help to you. It offers tips for overcoming various types of tone troubles. Here is the link:
3 Tips for Improving Your Tone
http://www.guitartricks.com/tutorial.php?input=474
Keep us posted - and good luck!
Best wishes, Lisa McCormick
Guitar Tricks Instructor
Lisa McCormick, GT Instructor
Acoustic, Folk, Pop, Blues
Full Catalog of Lisa's Guitar Tricks Tutorials
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Acoustic, Folk, Pop, Blues
Full Catalog of Lisa's Guitar Tricks Tutorials
Find Lisa on Facebook!