As fast as you dip it in the liquid, take it out. I realize you are using heAted milk but if there was ever a problem in a cookie falling apart too fast , it's because of that.
Try to dip it in cold milk and fast. With all the other liqueurs you are using , the cake will all come together nicely once the cake has set.
The lady fingers your mom used are probably not the same as what they sell today , reason why she had to soften them with warm milk.
The lady fingers today...