This is a very good question because it would seem that Amanda Wingfield, Laura's mother, would in fact want gentlemen callers for her daughter in order to relieve her own youth. However, that would reduce Amanda's depth of character to a much shallower type.
It is true that Amanda Wingfield's notoriety in the play stems from her tendency to recall her past, almost non-stop. Recalling the gentlemen callers, particularly, brings her excitement. It takes her to a time and a place when she is beautiful, sought after, and happy. Now, she is middle-aged, abandoned by her husband, and with two adult children who are lost in life. There is little to blame Amanda for it.
AMANDA: They knew how to entertain their gentlemen callers. It wasn't enough for a girl to be possessed of a pretty face and a graceful figure although I wasn't alighted in either respect. She also needed to have a nimble wit and a tongue to meet all occasions.
However, it would be unfair to conclude that the mere reason why she wants Laura to receive gentlemen callers, the way that Amanda used to when she was young, is simply to revive her own youth. Surely, a gentleman caller would bring the joy and excitement that the Wingfield household desperately needs. However, there is much more to Amanda's motherly nature.
There is plenty of evidence throughout the play showing that Amanda Wingfield indeed loves her daughter, Laura, and has put in a lot of effort in trying to provide a good quality of life for her. However, Laura's lack of self esteem (partly do to her leg malformation), and obvious social anxiety make Amanda's efforts go awry.
Amanda does want what is best for her daughter. She signed her up in vocational school only to learn that Laura was too shy to attend, and then dropped off. She asks Tom to bring Jim over to the house to see Laura, only to find out that Jim is engaged to be married. Amanda is quite worried about Laura, and about the family as a whole.
AMANDA [hopelessly fingering the huge pocketbook]: So what are we going to do the rest of our lives? [...] We won't have a business career - we've given that up because it gave us nervous indigestion ! [Laughs wearily.] [...] I know so well what becomes of unmarried women who aren't prepared to occupy a position. [...] stuck away in some little mousetrap of a room - encouraged by one in-law to visit another - [...] Is that the future that we've mapped out for ourselves? I swear it's the only alternative I can think of ! It isn't a very pleasant alternative, is it? Of course - some girls do marry!
Therefore, we can safely conclude that Amanda may certainly appreciate a gentleman caller or two in the house, for her own sake. However, she would much rather receive one for her daughter, so that her daughter's fate is at least partially secured by getting a husband.