When you (and your kids, if you have them) move into an already established household, you come in as an interloper. Never mind that you were invited or are there by mutual consent; you'll still have to deal with this issue of claiming the home as your own without appearing to be an alien invader.
Enhance the past with the present. Incorporate the “old” furniture into a new look. Mix `n' match! You cannot erase the past, so combine it with the present and move on into the future.
Claiming Your Space
You're the new doggy on the block, so it's time to mark your territory (in proper style, of course). Claiming space is touchy, especially if you or your brood is literally displacing somebody. Go slow. Wildly redecorating the entire house will feel like an emotional challenge to the stepkids, and possibly to your mate. You might want to shift bedrooms around, or at least reorganize the furniture, especially if this is a home where the ex used to live when the first family was all together. You'll feel more comfortable if you're not making love in the same spot—or same bed—where little Joey was conceived.
If the ex is deceased, the family might take your reorganizing and redecorating very personally. Be prepared for the kids to react. “But it looked better before! What did you do with our dad's shaving gear?” You do not have to live with the objects of a deceased ex's life. Tell your mate that you need support on this issue. Enlist the kids to help you pack the stuff. If they aren't ready to sort and dispose of the “effects,” invest in a small storage rental unit until they are (and this may take a few years).