Yes, move the picture frames -- they will not add any substantial weight to her shipment, and they're something you'll use at your new place. 
 
Any picture frame can be packed in a mirror/picture carton, or if small enough, it can go in a regular box.  The best advice on packing in a small box is to make sure that the frame is standing on its side, and not flat on the bottom so that weight from other items in box doesn't crush or break it. 

Here are some other tips on items that will be needed to secure artwork, mirrors, marble tops, glass tops, and pictures for moving:

1. If your painting is framed with glass, put masking tape across the front of the painting like an X to keep the pieces in place in case the glass breaks in transit.

2. Cover the framed painting with bubble wrap and tape it shut.

3. If you are packing a painting with glass, put the painting in a picture or mirror box. If two boxes are needed for the painting, put the second box on top of the other by telescoping them together and fill in any spaces with packing paper.

4. If you are packing a canvas painting (no frame, no glass), wrap the box in bubble wrap again, tape it, build a second box for the first box. Your chances of sharp objects puncturing the box and canvas during the move are slim.

5. Tape the box shut and mark it "Fragile - Art" along with some designation of where it will go in your new house.