Is the prayer valid with intense urges to relieve oneself (الأخبثين), and should it be repeated as a precautionary measure?

What you did by praying while suppressing the urge to urinate or defecate (haqin) was incorrect. However, your prayer is not invalidated as long as you performed it completely, for the scholars have agreed that the prayer of one who is suppressing urges is valid if he completes it. As for the hesitation regarding interrupting the prayer, scholars differed on whether it invalidates it or not. What you did by repeating that prayer was correct, as it allows you to avoid the differing opinions of the scholars.