I, too, don't think a letter will help.

Two things to suggest:

As Sunrise already suggested, try to get a different HMO. That's hard to do because your son and you will have "pre-existing" conditions that very well might make any other HMO reject you.

The other thing to do is see if the HMO will let you go out of network--and still cover the care--to somewhere in a more convenient location for you. It's not unheard of. Since you're in a big metro area, I'm assuming you could find something closer--outisde your own HMO network--that provides the services you need. There should be some appeal policy on that. Don't do it on your own, this is the time to enlist the various providers you work with to help you identify other places to go, and have them "recommend" them to you, i.e. have them write something--as part of your appeal for out-of-network coverage--on your behalf to convince the HMO that they can't meet your needs in-network due to the location issues and that what you need is to go to specific alternatives that theywill say will be best for you and your son's (mental) health. Start with a discussion about this possibility with your pdoc.