I'm a poly parent - I live with my GF and her husband, who have a four year old daughter (I'll call her Baby). She is now considered by all of us as my daughter too. I have been a part of their family for just over two years... so I can speak both as the 'other partner' coming in as a new parent - and as the existing parent dealing with 'other partners' coming into the mix.
From the side of being the 'other partner/parent' first....
Yes, absolutely. Both my GF and her husband have had moments of feeling threatened (even though they have always been hugely encouraging of the relationship between myself and Baby). Moreso Hubby, as he isn't in a romantic relationship with me. Baby is like my best friend - we adore each other. As soon as we met, I was a novelty to her. She often prefers to sit by me in restaurants, hold my hand when we're out, etc. We are very close. This could be hard at times for GF and hubby (understandably!!!). Of course this would upset them.
From *my* side, as the 'new parent/partner' (I'm giving this first, to give you food for thought), I have been eternally grateful for their approach to this. To feel their trust... their admiration... their appreciation for everything I do with and for Baby... it's honestly the most beautiful thing. I know, and they know, that I really do enrich her life. Not only does she have an extra person to love and to be loved by; but there are tangible benefits to her little life - and to GF and hubby's lives. They have an extra babysitter who they trust ~grins~. They have someone to give an extra hand with clothing her, feeding her, entertaining her, applying bandaids, dealing with tantrums. There are also unique things that I bring to her life, simply because of my own experiences and personality, and it makes me feel absolutely wonderful that GF and Hubby appreciate this.
However, still from the perspective of *me* as the 'new partner'. I've never, ever wanted, or dreamed of 'replacing' GF and Hubby as Baby's parents. They each bring countless wonderful and unique things to Baby's life that I couldn't bring so effectively. If we are good parents, nobody can break that bond. We also all can't be everything - I can't simultaneously be playful older sister, Auntie, Mother, Father, band member, fashion police, authoritarian, chef, etc. I can be a little of all of those things -but I excel in some areas and am complete shit in others. What does work is when the three of us put our skills together. GF is great with discipline and Baby respects that. I'm great with talking to Baby and helping her to express herself. Hubby is great with education and spoiling her
So, this brings me to the point worth considering. When we are threatened, it can mean that we feel a person is doing something 'better' than we are. Absolutely, it's usually to do with kissing or sex, on these forums. But of course it applies to parents too. I thought I was a rocking first-time parent over the past two years, until my platonic friend came on holiday with us. Pffft.... Baby totally shirked me! It was all about him! He was an absolute natural. She completely adored him. Now... because he is my friend, I didn't think much of it except "sniff, sniff, she's not holding my hand". If he'd been my GF's secondary, I probably would have been very, very uncomfortable.
What does that tell me? It tells me that I not only fear being replaced as a parent; but replaced as a family member. That's my shit to work on
Alright, so, moving onto *my* perspective as the existing parent.
We don't currently introduce Baby to our secondaries, for two main reasons. The first is that we are quite fickle wenches - our secondaries don't last long. We don't want her to become attached to them and then have them disappear on her, time and time again. The second reason is that we are protective - and yes, in turn, possessive - over Baby and the family unit in general. The model we have signed up to is that love and all that is great; but in terms of Baby and co-habiting, we'd like to continue as a V - myself, my GF, her husband. We don't want to move other people in or have the conflicting opinions of a whole group of people raising her.
Some of this, I feel, is logical. I do think children need stability and protection. But of course variety is great - of course a colourful and rich childhood, meeting many different people and losing many different people, could actually be extremely productive for her development.
Ultimately, to give you advice: there is nothing wrong with admitting that you feel threatened about other partners bonding with your child. There is also nothing wrong with adopting whatever model of relationship and parenting suits you. Where you have conflict is if you decide it's totally cool to have people over at your house, or even move in with you - but expect them not to bond with your child. It either has to be separate, or it has to be encouraged.
So, how can you work on your feelings of replacement, if you decide to involve other partners in your child's life? Essentially, think of the benefits to your child and you will find peace. Think of their happy little face. Then, think about what this other person is doing that you might not be doing and what you could learn from this. Do you recognise that you could communicate more with your child? That you could play with them more? Anything at all that you can see you could make an effort to do better? Or, is it simply the novelty of this new person? Their natural ability with children? Finally, what do you see that you do well, with your child? What do you already provide for them that you know they need and appreciate? All of these things will hopefully help you to feel more at ease.