In Genesis 16, Abraham and Sarah made an unwise decision simply because they became impatient whilst waiting. God took His time to fulfil His promise because He wanted Abraham and Sarah to be physically as good as dead (Hebrews 11:12) so God alone would get the glory. He was also increasing their faith, patience and building their character (James 1:1-4).
Ishmael is of the flesh and Isaac of the spirit (Galatians 4:28-29). Ishmael is man intended and God "permitted". Isaac is God promised and God fulfilled.
We can't afford to cling on to the past when God is preparing a bright future. Ishmael represents the past and Isaac, the future. Ishmael is the product of having a bond servant, Hagar. If we have Hagar in our lives, we need to surrender it to God. Initially, Hagar and Ishmael seemed appealing and satisfying but eventually Ishmael brought dissension into their home. On the contrary, Isaac brought laughter. Abraham tried to keep both Isaac and Ishmael in his home but realised that they were living in constant conflict. The time came when God said there was no longer room for compromise so Hagar and Ishmael had to be sent away (Genesis 21:12).
God's promise of countless descendants to Abraham can only be fulfilled as planned, through Isaac. Similarly, since God's promise to us can only be fulfilled His way, what then should our response be if we don't wanna settle for second best? Let Hagar go! :D