There shouldnt be any issues with merging a family as one. If you do things with your children as a couple, letting them know how you feel and ask them how they feel about sharing quality time together.

Asking them how they feel if you and the children move in with your partner as a family. Its important that you understand your childrens feelings and knowing they will have another dad/mom involved and letting them know that it won't take them away fromt here biological parent or replace them.

Understand your child(s) feeling and slowing move them into that direction.