There are so many directions I could go with this, but let me pick one, the one that I think is most important.
Right now you are in a "V" relationship. If there is no functioning relationship between the "arms" of the V then everything has to get put through the person at the "base" of the V. This has several effects - first, it gets filtered according to this person's paradigms. Stuff that you want to express forcefully may get softened, and less important things may get emphasized - not that this is done deliberately or with bad intent - we all have our own filters and paradigms that we have to work with.
Second, it puts the person at the base of the V under huge amounts of pressure to act as a go-between to resolve things. In my own personal experience this is nasty. Ever seen that old roman torture where they tie each arm of a man to a different horse and get the horses to run in opposite directions? That's about how it can feel.
You don't have to be friends with the person, you don't have to socialize with them. But in my opinion you do need a direct line with them. You need to be able to get direct feedback from the person as to whether they really understand your concerns, and you then have a chance to understand that person's concerns.
Discuss priorities for the relationship - and that includes time together, including "quality time" where the other should only make contact in a dire emergency if that is what is appropriate. What about vacations and holidays (ok, you can get Thanksgiving but we get Christmas). It also includes what I call "decency and privacy boundaries" - things that you regard as private to each relationship and things that can be talked about freely.
Putting all that stuff on the base of the V means that the result is often sub-optimal and the person at the base starts to resent the whole process, because they quickly get worn out.
The other thing that having this functioning relationship means is that, should something be not to your (or her liking) you can feel like you can get in touch with each other directly to work it out.
So this isn't about negotiating rules or anything like that, it's forming the basis of where you can work as a team to sort through issues, with a full knowledge of each other's boundaries and personal comfort levels. You can't really respect them (or expect them to be respected) if not everybody knows what they are.
Try to get to the point where you are thinking of the "third wheel" (a term you used) as on a tricycle (a part of the machine), rather than a spare wheel on a bicycle, added on for convenience, but not really necessary.
"Listen, or your tongue will make you deaf." - Native American Proverb