This is a long thread, I've just discovered it, and I have not read all the responses. But I wanted to give my perspective from back when I was in a similar situation.
Back in 1999, my ex husband and I opened our marriage. We had been married/living together for 25 years at that point. We had 3 young children (preteen and young teenagers).
My ex at that time finally accepted me being bisexual and poly in nature, and he decided he'd like to try for a triad (big mistake, but we didn't know any better). We met a woman who seemed interested. My ex told me if anything about the relationship made me too uncomfortable, I came first and he'd call it off.
So, he got with her... she said she was bi and interested in trying to be with me as well. But within a short time, it became obvious she really wasn't interested in women in general or me specifically, for sexual activity or any kind of emotional closeness, even.
Other strikes against this working out was that she lived far away, about a 6 hr car trip. So, for him to see her, it would take an entire long weekend, costing a lot of gas money. When he got there, he'd wine and dine her, which was expensive (and considering, back then, he and I rarely had long romantic evenings, or even dates out for dinners, movies, or music shows, this seemed unfair)-- not really in our budget.
Plus I didn't appreciate having him gone one or 2 long weekends a month, for our childrens' sake and because I'd be stuck with all their care and other household and pet care alone, as well.
Also, he and she were in extreme NRE, not well managed, and he was distracted and spending lots of time phoning and emailing her when he was home!
So, I gave it a good try. She'd visit sometimes, for a long weekend or even a week, and I'd take the kids out of the house so the happy couple could have sex... Which felt kind of sickening. I felt like the nanny. Also sometimes they'd leave the house (to "go get a video") and be gone for 1 1/2 hours, while I sat home with the kids and felt jealous.
So... after several months of this, I just couldn't take it anymore. She was jealous of me, as the primary, I was jealous of her, as the pampered, sexed up new gf. So, yes, I did veto it.
I allowed them to remain friends, and over the years they met from time to time at events with mutual friends. I'd stay home with the kids. They also emailed regularly.
Fast forward 10 yrs later... After much therapy with a poly friendly therapist, couples and individual, he and I separated, and 6 mos after he moved out, she moved in with him. They lived together for 18 mos and then she moved out! (Same things that bugged me about living with him, also ended up bugging her, after their long standing NRE wore off and reality finally hit.)
My point? Couples new to poly can and usually do make mistakes. Since I've been single I try to only date guys (or women) who are single, or preferably, if coupled, well experienced in practicing polyamory, managing their time, budget and NRE well. I also avoid dating people with young children.
Love withers under constraint; its very essence is liberty. It is compatible neither with envy, jealousy or fear. It is there most pure, perfect and unlimited when its votaries live in confidence, equality and unreserve. -- Shelley
Mags (poly, F, 60) loving miss pixi (poly, F, 38) since January 2009, living together since 2013
also loving Punk (monogamish, former swinger, 42, M) since Oct 2015
"Master," (mono, 34), miss pixi's Dom for 2 years