Is it permissible for my wife and me to perform 'Umrah without our two children (3 years and 1 year old) entering into Ihram or having the intention of 'Umrah for them, knowing that they will accompany us in all the rituals, and is it permissible to carry an infant wearing stitched clothes during Tawaf?

You are not required to perform Umrah for your two children, and it is permissible for you and your husband to perform Umrah without them. However, it is better for them to perform Umrah with you unless their participation causes a hardship that prevents you from completing your rituals in the most perfect manner. There is no harm in carrying a child during Umrah, and it does not matter if he is wearing sewn clothing, nor does it matter if he is wearing a diaper, as long as you do not know that there is impurity in it. If you know that there is impurity in it, then do not carry him, because purity from impurity is a condition for the validity of Tawaf according to the majority of scholars. Some scholars have permitted carrying a child even if you know of impurity on his clothes or diaper, as long as the impurity does not transfer to the person carrying the child.