I agree with Margoz that your happiness is important for your children and they will understand and support you getting married a second time. An honest conversation with them and respect to their needs and oppinion could help avoid any serious issues on your second marriage. Yes, their life will change and let's hope it shall be for good. Happy parents have happy kids :)
Contemporary families contain a child from a previous marriage, step brothers and sisters, biological and step parents and other in-laws called by name. Most children are familiar with that kind of relationship thanks to their classmates and friends and when it happens in their family they are not as stressed and shocked as we expect them to be.
I guess your children already know his children and they often play together. It won't be difficult to explain them that now you all gonna live together. That is the best scenario. Others involve long conversations with all future family members to explain what is going to change in your life and what is static, like the love you have for your children. Your children love you and your happiness is also important for them, be honest and tell them everything. They will understand you.
If the child is still an infant, it might not affect them as much before their memory of the trauma will be forgotten and become long-term memory. However, toddlers, adolescents, teenages and adults must be considered in any decision that the parents wishes to make, especially when new parents are going to be part of the picture. Ensure that the child is still treasured and loved in the second marriage or it could end up like the story of Cinderella, except princes these days rarely hold balls for the general public.
If the changes are sudden and without consulting the children, yes, they may feel like they have a loss of control over how the family structure will be, and as such may be very detached from the family and new parent. It is important to inform the child of any major changes before it begins so that they can adequately prepare themselves. The new potential parent should also aim to build a bond with the children so as to develop a sense of trust between them and the kids.
When divorced parents wish to remarry, their children may face certain issues. Depending on the age of the children, they may have difficulty adjusting, and most children will have difficulty knowing what to expect from a new step-parent or even step-brothers and step-sisters. The best advice is to give the children age-appropriate information and set their expectations for how things will go. Give them plenty of time to process the changes and offer lots of opportunities to ask questions. Make sure they know that although day-to-day life will change, your love for them will not. They will always remain important to you.