"That…Okay, but we will not be living there that long. The moment my friend fulfils his promise, Our family will be shifted to another place but you can still send your Prince to me, I will be honoured to teach the kids born from the boon of Mahadeva."
Drona took a moment to process the offer of Kripa. The logic and reason used by Kripa were impeccable, Even if Drona wanted to refuse he can't as Kripa did not ask him to come with him as a Brother-In-Law but as a friend.
If he rejects the offer of his not only he will hurt Kripa with this sentence it would also be an insult to the friendship they share, he did not want to lose that friendship, So he had to agree to put aside his pride for once.
It would also be hard to explain the reason behind the refusal as he was going to ask for help from his other friend, So there Kripa played his word game well not giving him a way to counter him.