A less reflective room is often better for recording audio, because it's easier to add reverb than remove it. The Transient Shaper that comes with Sonar is pretty effective for reducing reverb, just adjust it so the reverb tail gets cut down. A noise gate or expander can be useful as well, but if there's lots of reverb gating can sound like Phil Collin's drums from the 1980s. An effect that has its uses but possibly a bit much if on every vocal line.
I'd probably go for the smaller room with the carpet, but without hearing both it's difficult to say. Clapping your hands in a room is useful if you want to hear how it reverberates.
Controlling room reverb can be tricky. Thin absorbers like blankets or even thin acoustic tiles are really only useful at dealing with treble frequencies. Egg boxes, packing foam and similar do nothing at all. If your mother won't let you attach anything to the walls, might she accept a free-standing screen as OK? You can buy them but if they're any good they're heavy and expensive. But it's easy enough to build a cheap and effective one using a simple box frame made of timber with heavy sheet rockwool (the stuff used for insulating houses) in it with the whole thing covered in hessian to stop the fibres escaping.
You could then stand it somewhere a few inches from a wall or prop it across a corner of the room and record with your back to the frame and the mic reflection screen you already have on the other side of the mic to catch anything coming in from the other end of the room.
You might find these useful -
https://www.soundonsound.com/sos/dec07/articles/acoustics.htmhttp://www.soundonsound.com/sos/oct10/articles/qa-1010-2.htmhttps://www.youtube.com/watch?v=spg4y5_zsMs (video tutorials for building a frame for rock wool)