Hi Logar,
What I would do in your situation:
Ask your mom whether she prefers a commercially bought coop because it would look nice and finished, while a homemade coop could possiblbly look very rough.
I would say that commercial copps do tend to meet a consistent, acceptable, standard of finish, while homade coops can be all over the place as far as appearance goes. To some people, looks are just not important for a chicken coop. Others do make thier coops look very nice. (The files section of this site has pictures of some coops that I'd be proud to live in if they were people-houses. ;^) ) You could show some of those pictures to your mom and promise to set a high standard of finish for your coop and make it enhance, not detract from, the looks of your back yard.
As far as practical connsiderations go, this site is also full of posts from people diappointed with the comercial coops they bought. You could probablly easilly build a better-functioning  coop yourself than most of the commercial ones. Designing and buiding your own coop would also be a chance to improve your building skills, which will very probablly help you in future years when you have your own place to fix up.
PS: The commercial coops you mentioned are also very much on the small side.