Is a marriage contract valid if nine years have passed, it has resulted in two children, the husband does not recall the wording of the contract, and he doubts whether he was questioned by the notary?

Your marriage is valid, and there is no need to renew it. What you doubt regarding not remembering uttering the صيغة العقد (marriage formula) is from the whispers (waswas) that should be dismissed. The general practice is that the marriage officiant (ma'dhun) prompts the husband and the wife's guardian to pronounce the marriage formula. Just as doubt after completing an act of worship is not given attention, it is apparent that the officiant completed all the marriage procedures. The confirmation from those you asked that the officiant prompted you both with the formula further confirms that what you are experiencing is due to whispers (waswas).