Welcome to the forums!
There are many people quietly "doing" poly that you would not suspect. In ways that vary widely but work for the people in them.
Your "family" model seems similar to my own - although my boys are not involved with each other, they are best friends - we teasingly use the term "brother-husband" on occasion, but it really does feel that way at times.
Sounds like you've already cleared the first hurdle that many would advise - letting the relationships mature before making a rash decision to move someone in. After a few years, you all probably know each other pretty well. (NOTE: we did NOT follow this - Dude moved in right away, just like, 19 years earlier, I moved in with MrS right off the bat - just because I didn't follow it doesn't make it not good advice.)
The next hurdle seems to be the practicalities of actually living together - a stress on even regular old dyad relationships. It's good that she has spent extended time there but "most weekends" is not the same as "24/7". It is moving from "family friend" and "comfortable guest who gets her own drinks" to "full-time family member" - without 5 days in your own space to recover. Another common piece of advice (that we also don't follow) is to make sure that each person has their own personal space and alone time. (We have a small house and one bedroom - with a BIG bed - luckily I am the only one with "alone time" needs and everyone sleeps on different schedules so it all works out.)
One thing that should probably discuss (ad nauseum) is household responsibilities/expectations. If there is a disagreement (even over something simple) how is it resolved? Does the final decision rest with the "original" couple? Do you two girls hammer it out and present him with a decision or put him in the position of "tie-breaker" (hint - don't put him into a position where he has to choose between you on stupid shit - only badness can ensue.)
What role does she have in raising/disciplining your child? "Favored aunt" has different expectations than "third parent". (I don't have kids so I'm sure their are issues here that I am unaware of)
What if she wants to redecorate/rearrange the living room? (We each have rooms in the house that are "ours" to determine the furniture and decor - I don't bitch about how they want to do the TV/computer-room - a.k.a. "man-quarium" - and they don't have any say about how I want the library/livingroom)
Do you all agree on one brand of shampoo or are there 3 bottles in the shower? (MrS and I don't care - so Dude gets whatever he wants since he does most of the shopping - and buys in bulk)
Who is responsible for washing the sheets? (We each do our own personal laundry and I do the bedding/towels).
How are finances covered? (Our system is somewhat complicated but works for us - I have final veto, as I earn the bulk of the $)
Above all, I guess I would add - don't make assumptions, even (especially) ones that you think are really obvious. Ask. Discuss. Clarify.
Recently the three of us have opened our relationships with each other based on some established ground rules.
I would be interested in hearing more about this. Our "rules" are - condoms if sex with anyone other than the three of us and keep the others in the loop if relationships are evolving with outside people (this is more for Dude - MrS hasn't pursued any "outside" relationships/sexual encounters that I haven't instigated in the 20 years that we have been together, my female FWB arrangements have also been stable for years). There are other rules that have come and gone as we adjusted to our poly situation (for instance - from me - "don't chase me out of my own bed to have sex with your ex-girlfriend because you think I want a threesome and you never asked me"
and - from MrS "don't have sex in the bed, while I am in it, if I am asleep - move to the couch")
Are you talking about rules between the three of you or rules concerning outside people?