My opponent comes in with with 11 might against my 4 Spiderlings that are 4 might each. If they deal 4 damage to 2 Spiderlings and 3 might to another, will the 3rd Spiderling also die when the first two Spiderlings die?

No — the third Spiderling lives; 3 damage on a 4-Might unit is not lethal when the kill check happens, and the 3 damage is then healed away.

The Combat Cleanup's kill check evaluates every unit at that one instant, when all four Spiderlings are still in play and therefore still 4 Might each (1 base + 3 for the other three). The two with 4 damage die simultaneously, and nothing re-checks the survivors mid-task — the same Combat Cleanup then heals all units in play (Rule 468.1.a.1), wiping the 3 damage before any second pass could see the remaining Spiderlings drop to 2 Might (Rule 322).

Your opponent's 11-Might assignment itself was legal (4 lethal to one, 4 lethal to the next, 3 left over on a third — CR 467.2.c.3/.4). Worth noting the edge case: if that 3 damage had come from a spell or ability instead of combat, there'd be no heal, and the follow-up cleanup would kill it once its Might fell to 2. In combat, it survives -- and the four Spiderlings deal 16 back, so the 11-Might attacker dies.