A personal therapist acts only in the interests of their client..... at the clients own pace.... it's not the therapists place to go digging around in search of "understanding", especially in places the client doesn't want to go.
In the "safe and trusting relationship" of therapy the therapist may appear to "be on your side", but that's very different from "taking your side", which not what therapy is about. A therapist who thinks that meeting you family for one or two hours can "clear some of the crud out" is deluded. Family dynamics are complex and deeply entrenched in the participants backstories.
A personal therapist who meets with a clients family members is already on thin ice, to do it when their client is uncomfortable about it indicates they've fallen through the ice taking their client with them. Once that's happened it's very difficult to get the personal therapy back to solid ground.
If something like this goes ahead, both you and your therapist need to be VERY clear about the purpose, much more specific that "clearing out the crud". What crud EXACTLY.... how might the meeting change things, what are the risks, who is in control of the process? Just exploring these questions can be fruitful, regardless of whether a meeting eventually occurs, and if it does you and your therapist will be much clearer about why it's happening and what are the markers of risk.
One other thing..... make sure your therapist has gone for supervision about this, ie consulted one or more colleagues who know them well, ideally in a group context(eg within their practice), to explore the issues. For me, supervision is an important marker of the good therapist.
