BklynMama, I would want my family ped to have access, to be on record as our family doctor, to get DC's records forwarded to her, etc. I would want a doctor that *I* picked (one who at least understood my desires and philosophies) to be involved in my child's care. I'm not sure she'd need privileges at the hospital to have that though.
If I was transferring, I would def. want a Level III NICU on-site, so Mt. Auburn is out for that reason (as well as others, see below).
The OBs I spoke to at MGH were universally extremely negative about homebirth. I don't know how they are when patients transfer. The attending ped on the L&D recovery floor when I was there (two years ago) was pretty daffy, and their LC was awful. These things may have changed (among other things, when I was at MGH last winter, it appeared that they now partner with Isis Maternity for childbirth prep and lactation consultants), and I know nothing about the staff at BWH (which has been partnered with Isis for quite some time). My anti-MGH bias may not be entirely justified, especially if you'd only be transferring there in an emergency.
When I was talking to midwives, they all seemed to think that Brigham & Women's was the best choice for homebirth transfer if you needed it. They were not thrilled with Mt. Auburn (it's apparantly great if you plan to deliver there but doesn't deal with HB transfers so well).
My temptation would be to plan to transfer to BWH if necessary (because of the midwife opinions), and to request that NICU staff keep your ped informed, so you can ask his or her input. All of these hospitals (except for Children's) are part of the Partners network, and one thing that network does really well is share information. If your ped has access to MGH's patient records systems, those should be integrated with BWH's systems.
Finally: While Children's has a well-respected NICU, they don't offer any obstetrical services, so they are accustomed to transferring babies in. You might ask your ped what it takes to transfer a baby from BWH to Children's. They are, as you note, right across the street from each other.