It was originally Sarai's idea., but there were things she hadn't expected. It was apparently not unknown for a barren wife to produce an heir through a dependent surrogate. There are legends that Hagar had been given to Abram when they were in Egypt, for just this eventuality. She didn't act like a respectful underling, and Sarai wanted her gone, not only before Ishmael was born, but later, as Sarai (now Sarah) had had, through a miracle, her own son Isaac. Abraham went along with it; he head to deal with both moms, both fierce and protective. Sometimes I wonder if it would have been possible for these brothers to have grown up together in peace, but we still live with the reality of this rivalry.
We see another one, later. Bathsheba was the last one of King David's eight wives. (I notice that when we read of polygamy in Scripture, it is associated with trouble!) When David was on his deathbed, his oldest surviving son Adonijah (son of wife #5) , set up coronation festival for himself in Hebron, his birthplace. He did not invite Nathan the prophet and his half-brother Solomon. Nathan went to Solomon's mother Bathsheba, who went to the King, and reminded him that he had told her that Solomon was to be his successor. David abdicated in favor of Solomon; Bathsheba did try to do Adonijah a favor to smooth it over, but Solomon saw it as a threat.
Even Jesus had to deal with a pushy mama. In Mark 11:.35, we read that James and John came to Jesus, asking for positions of prominence in the expected Kingdom. In Matthew 19:20, we see their mother coming with Jesus with the request. We don't know if it was one occasion or two, but somehow it's not surprising that Mom had an interest. Jesus uses this request as a way of introducing a major teaching: that His Kingdom is not about authority or precedence, but about service. The Bible is amazingly honest about the people whose stories it tells; we see more feuds and power grabs than selfless service; just like the real world we live in--but Jesus came to change the world. Which world do we want to live in?