Why does the Lord plan on hardening (The Hebrew word translated “hardening” means "to make strong,” i.e. to strengthen Pharaoh's resolve.) Pharaoh’s heart? Doesn’t that seem to undermine the purpose of Moses’s mission? Leon Kass is helpful:
These questions, if they occurred to him, do not detain Moses from beginning his journey. But we will tarry over them a little, for they can illuminate the meaning of subsequent events in Egypt. Our perplexity diminishes once we recognize that getting the Israelites out of Egypt is not the only goal or even the most important one. How they are delivered, and by whom, matters almost as much: If Pharaoh freely and easily let them go, would not he, rather than the Lord, be seen as their deliverer? There are also considerations of justice: shouldn’t the Israelites’ deliverance from Egypt involve retribution for their lengthy oppression? Finally, there is a decisive issue of knowledge: shouldn’t the Israelites—and the Egyptians, and also we readers—learn from their deliverance about the powers that be? Shouldn’t they (and we) learn who or what is highest and mightiest, and who or what governs the world and the people in it? For hundreds of years, the Israelites have lived and suffered in a society ruled by a single human master—an autocrat who is both feared and revered and who thinks and acts as one of the gods— atop the world’s most advanced civilization. To correct their way of thinking, they need to witness a protracted contest between the Lord and Pharaoh through which he and all of Egypt are compelled to acknowledge the superiority of the Lord. Only in this way can the enslaved Israelites learn that Y-H-V-H, their God, is indeed God Almighty.
But if the contest is to be conclusively revealing, there must be no easy victory over Pharaoh. He must be at the top of his game and must not fold his cards too early out of fear or weakness. Pharaoh must remain Pharaonic at the highest level, both to reveal the full meaning of Egypt and his despotic rule and to provide knowledge of the Lord needed for founding the nation of Israel. Thus, Pharaoh must not become dis-heart-ened. If he cannot strengthen or harden his heart by himself, the Lord must help him stay true to himself to the bitter end. Only in this way can the differences between Egypt and Israel, and between the rule of the Lord, be brought clearly to light. —from Founding God’s Nation: Reading Exodus, by Leon Kass
So, the Lord is giving Pharaoh over to himself, not making Pharaoh act against his will. To put it another way, Pharaoh is becoming more of what he already is. The ambiguity in the language reflects this: ten times (including here) we are told that the Lord hardened (or “strengthened”) Pharaoh’s heart; three times we’re told that Pharaoh strengthened his own heart; six times we are just told that “Pharaoh’s heart remained strong.”
The key to understanding the strange episode of the Lord trying to put Moses to death and the circumcision of the son is to note the mention of the “firstborn” in the passage. The Lord calls Israel his firstborn and says that if Pharaoh refuses to let Israel go, then he will kill Pharaoh’s firstborn. When the event comes to pass, it is the blood of the Passover lamb that protects God’s people. Here it is the blood of the covenant of circumcision that protects Moses’s family, and it is his (non-Hebrew) wife who saves him!
“Once again it is a woman who, by her quick-wittedness and insight, saves Moses. [Zipporah] stands in the train of the midwives, Moses’ mother and sister, and the daughter of Pharaoh. Moses owes his very life to a series of actions by women, two of them non-Israelites. ... Moses is thus revealed as one who does not himself stand without need of mediation with God.” —from Exodus: Interpretation: A Bible Commentary for Teaching and Preaching, by Terence Fretheim
What Zipporah does here is fully pledge her and Moses’s family to the covenant of Abraham. They are now fully God’s people, ready to be used to free God’s people.