I would ignore the biting. I mean, it's you doing something she doesn't like (picking up/relocating), she should not learn that biting gets her what she wants, that is, putting you in your place. Instead I would give her a treat (I use their pellets as treats, they don't get much of those, they go bonkers for those) right after putting her in the hutch, putting her face right to the bowl when you put her down, so she has something better to do than being angry.
Some of mine that hate being touched nip when I hold them too long, or bite furiously when I need to force feed them or cut something out of their fur or such, some sweaters and a winter jacket take the brunt of the onslaught.
Is there any way to connect the play pen with the hutch? I use ramps to let them in in and out, you could use low fencing, cardboard tubes or wooden tunnels for a path from the hutch to the pen. I use their pellets as treats to train them to go where I want them, most listen to commands though (although not instantly, it can take some 5 minutes to make up their minds)