If Edward could affix his brother's soul, why not his mother? Did it require seeing the 'truth' to do so? Does that mean the other empty armor suits (Barry) had another person who had seen the truth affix them?
Edward couldn't affix his mother's soul, because she was already long dead. It isn't made so obvious, but actually a few years pass between the mother's death, and then the boys training with Izumi, before they try and resurrect her. He was able to attach Al's soul to the armour because it was still present, in the body of the creature they tried to transmute. The mother's soul had long since departed, and couldn't be used in alchemy.
When the mother died of her illness, we can assume Ed never considered putting her soul into another object, and even if he did he wouldn't have known how, and probably would not have had the alchemical skill to do so anyway.
Because he didn't know how to at the time.
When Ed and Al first tried to bring their mother back and Al was lost in the 2003 series, when it shows him working to get Al's soul back, he says to himself that he didn't have much time. Later, when someone (probably Winry or one of Mustang's team) sees the seal on Al's armour and asks if it was blood, he confirms it's his own blood because he didn't have a lot of time. This would indicate that the soul's passing through the Gate needs to be recent, if it is to be bound to an object.
Secondlly Ed would eventually learn that the seal is by no means a long term solution
Although never mentioned in the 2003 anime there is an even greater danger; if one's soul is bound to an inanimate object for too long, the soul and object will eventually start to repel each other. The person will start to experience moments of exhaustion, which cause that person's soul to disappear from the object, as stated by Al, who compares his body to a time bomb. This can lead to the complete destruction of the soul as it slips away to The Gate. This makes the blood rune only a temporarily effective technique.
Source: Blood Rune - Negative Effects
Remember that in the Brotherhood series the time since Al was bound to his Armour is between 2-4 years. (There are 2 years between their attempt to bring back their mother and Ed going to Liore, and however long the series progressed until Al compared himself to a time bomb, which I roughly guess to be 2 years.) Thus, this would only give Trisha a couple more years to live.
Finally even if Ed knew the process and accepted the limited time Trisha would have as a soul bound to an object, a soul bound to a suit of armour is not what they wanted. They wanted their mother fully restored back to how she was. Remember that one reason for their search for the Philosopher's Stone was to restore their bodies, and that Ed always said the first person to be restored would be Al, even if Al gained some benefits as a soul bound to armour, which Greed (mistakenly) revealed.
A person whose soul is bound to an inanimate object feels no pain, hunger, or fatigue, thus enabling them to perform immense physical feats. Also, as the person has no body, he or she can sustain more damage than normal humans, placing the person in a state of high invulnerability.
Source: Blood Rune - Positive Effects
Few thoughts, that were not covered in existing answers.
It seems, that manipulating souls is actually not common knowledge in alchemy, since it was not even practiced much. Aside of Alphonse, there were only two subjects, whose souls were attached to objects, both created by scientists, that were researching philosopher stone. Even if Ed and Al were able to recover some knowledge of human transmutation, there was no way for them to learn, how to manipulate human soul.
Taking that into account, I'm pretty sure Edward didn't know how to attach soul to object until the very moment they opened Gate of Truth. It was actually knowledge he received from Truth, same to his technique of transmuting without circles.