Is it permissible for sons and daughters from different marriages to live together in one house after marriage?

There is no Sharia obligation to refuse marriage to a man for this reason. However, each of you has the right to refrain from gathering children in one home, except in special circumstances. If you both agree to them all living together, there is no harm. But it must be noted that your children are not mahram to this man's daughters unless there is fosterage (through breastfeeding), and Sharia guidelines must be observed, such as hijab and the absence of khalwa (private seclusion) between adults.