If you want to upload the source set of raws to www.dropbox.com and post a link to them, here, then someone can try and see what happens when they merge them.
Seeing the results of a merge isn't really enough information about what you've done to produce the results. The HDR merge DNG can be adjusted in LR the same as any raw file so a question would be why isn't doing that adjustment good enough?
If some of these questions are answered on a forum thread, then can you link over to it?
No matter how dark are the original pictures, my result is very white with useless photos. It used to be fine until 30 days ago. I just updated Canon's firmware *today) but problem remains the same. Could anybody tell me how can I solve it? I REALLY appreciate it! Thanks! Fer
Original 1 https://www.dropbox.com/s/63hbns0lg0y6h3s/Test%202%20first%20photo.jpg?dl=0
Original 2 https://www.dropbox.com/s/2a7gvi7p8824iqj/Test%202%20second%20photo.jpg?dl=0
Merged result: https://www.dropbox.com/s/z8zam6vmdeiazyl/Test%202%20MERGED.jpg?dl=0
The way you made one brighter than the other was to add artificial light, but the HDR process doesn't know about this, all it can do is normalize the values from each photo based on shutter, aperture and ISO. I think this is why the result is brighter, because the HDR process brightened the slightly dimmer one because it was a smaller ISO.
For these particular photos, just use the dimmer one and adjust it as needed. This will avoid the shadow on the ceiling and the second artificial light reflection to allow a clearer view of your companion, assuming that was the purpose.
Several other non-optimal things are apparent in these images:
1) For HDR, the scene should actually be simultaneously too bright and too dark to be captured in a single photograph. This one seems to be ok, other than the light-bulbs which is typically ok to have clipped. If we could also see out the window and it was significantly brighter, maybe an HDR would be needed.
2) You should be shooting RAW to capture the widest range of values, not JPG.
3) You should be varying the shutter speed or ISO to change the brightness of the scene rather than using varying amounts of artificial light.
4) The two images should actually be significantly different in brightness, not almost the same. One should be bright enough to capture detail in the darkest areas and the other should be dark enough to capture detail of the brightest areas. If the scene has a very wide range of brightness values, then sometimes another image midway between the other two might be needed but usually not.
5) Why are you, your camera and flash, and your companion reflected in the mirrors? Is this on purpose, perhaps because this is your house and you want people to be able to see you in the image, like a selfie camera bubble or postage-stamp in the corner of a travel photograph taking with your phone camera? Or was this an accident? If this was an attempt at real estate photography then neither you nor your equipment should be visible in the mirrors. If this is for personal use, then fine, if you intend people to see you.
6) The placement of the secondary light source you used to make the brighter image more bright is offset by a foot or two from the camera lens, and besides being able to see the reflection in the mirror, there is a shadow around the lighting fixture on the ceiling. Both the glare in the mirror and the shadow are only in one photograph so it might cause issues if you try to combine the two photos, besides looking less than optimal.
7) This scene has mixed lighting, overhead is reddish incandescent and out the window as well as the artificial light are more bluish daylight. I would suggest either waiting until dark so you only have the incandescent or turning off the lights and only using the daylight-thru-the-windows and non-flash daylight-balanced artificial lighting that is out-of-frame and diffuse so as not to be noticeable in any reflection or shadows.