But there is an issue of time and attention. I've run into the phrase "love is infinite, time is not" on poly sites and I think its an important thing to bear in mind.
I have a young daughter, age 6. and my second relationship does take away from time spent with her. Fortunately for me, my daughter loves the fact that mommy being busy means she gets to spend two nights a week at grandma's house. If, however, my time with my boyfriend interfered with my ability to take care of my little girl, I would have to figure something different out. And, yes, the boyfriend might have to suffer, but he has always known that I have obligations that have to come first.
If the OP's partner is not spending enough time with the OP and with their child, then it is up to the partner to find that time.
That time does not have to come from time spent with the new partner, though it could. The new partner is irrelevant. The OP's needs and the needs of their household and child are what is relevant. It is up to the OP's partner to figure out how to juggle these things, though all involved should try and help figure these things out.
Nightwalker, try couching your requests in terms of what you need and aren't getting, what time you need and so on, and not in terms of the new partner. If you have insecurities, address those.
My advice is to make it about you and your child, not about the new partner and give your partner a chance to make things good without causing pain to this third person.
You did agree to this, and you have, by proxy, a responsibility to not renege on the deal. BUT your partner has made a deal with you, and if he/she is not keeping up their end, you have a right to have your concerns addressed.
Just make it about your needs and those of the kid and let your partner figure out where the time is coming from.
Your partner may be having a hard time regulating NRE (new relationship energy), which is a concern you can address. It's normal and common, and it's your partner's responsibility to make sure the established relationship is being tended to properly, especially when there is a child involved.