Congratulations on your marriage! You're showing great foresight to be thinking now about how to facilitate this transition for everyone concerned.
1. Be aware that the move itself will be a big transition. The more you can ease into it, the better. If you are moving into his house, then spend lots of time there now, including meals and nap time, so that she feels comfortable there.
2. Be aware that your daughter is likely to miss her grandmother. Be sure to build in regular visits.
3. Three year olds can't really envision a move. I recommend you make a book for her. Take photos, print out captions, glue them to paper, get it laminated, three hole punch it, and tie it with a ribbon or put it in a notebook. The pages should start with your daughter as a baby, with you holding her and saying how happy you are that she is born. Then show a photo of your mother's house, and her at age two months, with you and/or Grandma. Add photos of her at the house doing things she loves. Then put in a photo of her stepdad with the two of you. The caption might be something like "Then we met _____ and we all loved each other. We decided to make a family together and live together." If there is to be a wedding of any sort, including a Justice of the Peace, be sure your daughter is there and in the photos, and include some photos in the book. Then have photos of his place, with her in them, enjoying herself there. Include photos of him holding her, and all three of you having fun together. End the book with a photo and caption "Our Happy Family." Start reading the book now.
4. Have lots of discussions now with your fiance about your child-raising philosophy. One of the most active letters pages on the Aha! Parenting website is the page where women talk about how the man they married was so nice to their child until they moved in together, at which point everything fell apart. (My Husband Hates My Kids.) I am not saying you will be in this situation, just that NOW is the time to discuss all those pesky issues like discipline philosophy, whether she is welcome in your bed, etc.
5. Don't let your husband discipline your daughter. This is an inappropriate role for step parents.
6. Encourage your fiance to play with your daughter as much as possible to solidify their relationship. Stay nearby but not involved. Over time, begin stepping back more and more, meaning go get a load of laundry, or take a shower, or even, eventually, go to the store for ten minutes. But that is a long way down the road, once your daughter has shown you that she can handle it.
7. Make sure you are spending daily Special Time with your daughter to stay connected throughout this big change. Play with your daughter in ways that allow her to surface any feelings she has about this. For instance, use a dollhouse or stuffed animals to have a mom, daughter, and new dad make a new family.
8. Your daughter will have some big feelings about all this. She may regress, for instance in potty learning or night-waking. Expect that, take it in stride, be patient. She may get "owies" or over-react to small things. If she acts out and you don't know why, she may be asking you to help her with her feelings. Set a firm, kind limit ("We don't throw toys") and then hold her while she cries.
9. Make sure your daughter always feels included, never pushed out. If you and your husband go to hug each other in the kitchen and your daughter pushes between you, enlarge it into a family hug and welcome her by saying "I'm the bread, and you're the bread, and HERE's the peanut butter and jelly!" Of course your intimacy is important. Don't worry. She knows who the married couple is. She needs to be sure there is still enough love for her. Your relationship is certainly big enough to include her.
10. Try not to initiate other new changes. Delay starting a new school if possible. Delay trying to get pregnant again. Be sure to bring whatever she loves from her old house, as much as possible. (And of course, let her make as many decisions about her new room as possible.)
You can expect some challenges. But if you just remember to keep empathizing with your daughter's perspective, love will get you through. Good luck!