I'm curious if any of you feel jealous about your metamours spending time with your kids. Also, how do you decide it's ok to accept a metamour/paramour as part of your family and get them involved in co-parenting? Do you consider potential instability a huge risk in child development or not so crucial?

My wife/np and I have been polyamorous since we met over 7 years ago and we've often discussed co-parenting being an advantage of polyamory but now that it is becoming a potential reality, I'm starting to get uncomfortable about it, mostly because it's happening so quickly.

Also, I'm concerned that if their relationship doesn't work out, it's going to contribute to some instability in our kids' life. Our daughter's daycare recently went through several new teachers in a few months and my wife also agrees this is not healthy for our daughter who needs to feel safe to learn and grow. I believe stability is very important to children's development.

She's been seeing my metamour for just over 2 months now. About 2 weeks after meeting him, she already introduced him to me and the kids at a playground. It went well and he and I connected nicely. Since then, with kids we have visited his apartment complex (swimming at the pool) a few times, he's met us at playgrounds a few more times, we've gone on beach trips twice, and we invited him over for dinner once at our place, so we are spending a lot of time all together as a family.

My kids are rather fond of him and even our youngest is getting comfortable with him.
In principle, everything is actually fine and I have no reasons to feel uncomfortable about him specifically. We also almost have a triad-like relationship and I feel really comfortable spending time with him and her together.

We regularly do other activities together without the kids and while we're together, just the three of us alone or with other adult friends, I don't feel jealous of him showing affection and or even more intimate displays of affection (sexual). Nor while they go on dates without me.

They generally avoid displays of affection in front of the children beyond what's typical of friendship (they did twice hold hands while walking behind me pushing the double stroller which for kids is surely not an issue but for me this says "romantic/sexual partners").

I am concerned that things are moving too quickly in the direction of co-parenting/family polycule, and a few times my wife has actually disrespected boundaries I've asked her to respect. (In fact, the disrespect of boundaries is what most bothers me.) She apologizes afterward and I have agreed to most activities beforehand but there are a few things that I'm not ready for and I wonder if it's just jealousy or if I'm being reasonably cautious.

Examples of her disrespecting boundaries:

1. The first case was: when I asked her not to have him hang out with us while the kids are around (after the first two meetings I felt it was moving too quickly), he met us at the park again without her asking me first. I've since then gotten used to him spending time with us and the kids at least twice a week, but every time one of these boundaries of mine gets disrespected, I feel bad and start getting jealous of him becoming part of our family so quickly.
2. While I was on a date, she invited him to our house after the kids went to sleep. I was unhappy with this because I'm concerned about the kids waking up and finding him there without me at home. After I told her I wasn't comfortable with him being there without me, she apologized (but also tried to defend it as harmless.)
   Our oldest is 4 years old and we've never had anyone stay the night without one parent home, and the few times it's happened, they've only ever slept separately from us (e.g. couch bed). I'm also concerned the neighbors could gossip. (We live where I work and I'm not comfortable coming out as polyamorous in a work environment.)
   There is an unfair balance due to her breastfeeding our son to sleep and generally not being able to spend a lot of time evenings with him but she can see him for longer periods of time on weekends and he has his own place. Sometimes my metamour waits for her after a date and she meets him nearby after the kids are asleep. I always help with bedtime - bathtime, bedtime stories with our 4-year-old (twice my MIL was there to help while I went on dates). However, it's quite difficult for me to put our son to sleep so far, so she has to rush home if he wakes up after she puts him to sleep (usually not until around 11-12 at night though. We're planning on weaning him soon.
3. Yesterday, we spent the whole day with my metamour and she invited him to hang out with us with the kids at the park afterward without asking me first. After I told her I was tired, had a headache, and a sunburn (we woke up at 5 am) she mostly ignored me until it was too late to cancel (he got takeaway and was already on the way) and then ended up including him in our plans at home after the children's bedtime without asking me. While I was driving to put our daughter to sleep, he came over to help her put our son to sleep even though I objected.

I'm going away for a few weeks end of August, so the question has come up whether he can visit her at our house after the kids go to sleep (or in general?) and I'm not comfortable with him being there with the kids/with the neighbors possibly knowing he's there without me. However, I do feel it's unfair that she most likely won't be able to have any time alone with him while I'm gone due to the lack of a nighttime babysitter (her mom doesn't know we're polyamorous).
Should I ask her to respect my boundaries or just find a way to get over my discomfort and let her have him over while I'm gone?
Would you consider this too quick for someone to take the first steps toward co-parenting?
Or am I just being jealous and too cautious because they're my kids?