When a couple gets married for the first time, they generally have no concerns about children from a previous relationship. They are starting with a fresh slate of their own, and their family will be assembled as the years pass. For those who have married someone who already has children, learning to coordinate everything that comes with being a new parent can become an experience all its own. It will require learning many new things, and patience is often one of the most important lessons.
It would appear that patience with the children is important, but it is also good to have it with the spouse who is a parent. They are generally not used to handing over any responsibility for their child except for their other parent, and it can be a difficult time for them. They will need to be able to integrate their family with a new person, and learning how to balance it all out will take time and trust.
Children are often the most adaptable people in this type of relationship, and most of them will be able to adjust well before any of the adults. As long as they find their lifestyle will change little, they are usually willing to accept another person into the household. There can suddenly be friction when their new stepparent asks them to do a chore they dislike, or it can flare when they are discipline for an infraction of the rules. It is at this time that patience becomes most necessary.
Being a good stepparent is a learned behavior for most people, and it takes time to develop. Learning when to say yes is just as important as learning to shunt the decision to their biological parent. Being able to make the adjustments necessary takes time and patience, but a healthy and growing family will be the result.