Is it permissible for the younger brother to propose to his maternal cousin, knowing that her mother once held her maternal cousin, who is 25 years older than the suitor, and put her breast in his mouth, but she did not feel that he had suckled from it?

It appears your mother did not confirm nursing your cousin, and the default assumption is that no nursing occurred. Even if she nursed him once, prohibition is not established, as the preponderant opinion is that nursing does not prohibit marriage unless it consists of five full, satisfying sucklings. And if we assume your mother nursed your cousin five full, satisfying sucklings, it is still not forbidden for you to marry his younger brother unless you both shared nursing from one woman with five full, satisfying sucklings.