Actively and happily poly for 8 years here… Be prepared for lots of monogamous people who will come here just to say how 'wrong' non-monogamy is/gullible you are/what did you think would happen etc.
In other words, this is not a very non-monogamy friendly environment and you might do better to find a Facebook group (there are a few) where you'll get a more helpful discussion… BUT ANYWAY...
First thing: he has cheated on you, in that he had a relationship that he kept secret from you. Open relationship or not, if your agreement was to be up front and honest with each other about who you were seeing, then not doing so is breaking your trust. So regardless of what happens next you need to think about how you rebuild trust, which starts with him acknowledging that what he did was cheating.
Second thing: banning each other from developing feelings was never going to work out long term, and expecting either of you to walk away from any relationship when you start to develop feelings is neither ethical nor likely to work. It's not ethical because it doesn't consider the feelings of the other person involved and not likely to work because you are humans, and when feelings develop is precisely the time it will be hardst to walk away. So one day it was bound to happen.
(For clarity, my nesting partner was in an open marriage, our relationship was supposed (for both of us) to be just about sex, we fell for each other and it was a lot of work for everyone to renegotiate the terms of all the relationships involved… My partner and his wife had never considered the possibility that either of them might 'catch feelings' either – which is astonishing looking back, but actually a fairly common scenario…)
So what next:
If you want to simply have sex with others without any risk of this happening then you'll need to explore something more like a 'swinging' setup, where it's just sex, nothing more, and usually not with the same person regularly.
If you want to be able to enjoy other aspects of relationship with other people: intimacy, conversation, basically anything that's not just sex, then you're going to have to agree ethical, reasonable and realistic boundaries for each of you.
For clarity: "you're not allowed to fall in love" is a rule, not a boundary, and it's neither reasonable nor realistic.
Reasonable boundaries might be around the amount of time he's away from you and your young child per week, and what kind of interaction you wish to have with other people he's in relationships with.
But all these boundaries can only regarding you and him - you can't make boundaries on her behalf about what she's allowed to do and not do without her involvement and consent, and you must always remember that she's not an addendum to your relationship, but a real person in her own separate relationship with your partner, and with her own feelings and needs.
The backdrop to all of this is that in non-mongamous relationships you all need to work extra hard to ensure that all the people you're with feel valued and loved for who they are. Especially when you're in the throes of New Relationship Energy, and all loved up and excited about a new person - it can be easy for your other partners to feel less cared for when there's a new shiny thing in town which is distracting you.
It seems to me that this is what has happened to you - that your partner has been so immersed in NRE you're feeling like he doesn't appreciate or want to be with you any more. But NRE does settle down – so naming it, and telling him how his behaviour over this time has been making you feel is really important. He likely hasn't noticed he's been treating you differently at all.
Also, as a final note, renegotiating the terms of your relationship when you're tired with young children – which will have already changed a lot of things for the two of you – is really tough.
You can't change what has happened but you do need to take things slowly and carefully, and be honest about what you need and what you're both capable of giving to each other and to other people at this time in your lives.
Above all you need to start communicating openly, honestly and non-violently, and start thinking about the kind of relationship you both want with each other. Have you read any books about polyamory or non-monogamy at all? Because they can really help...
And finally: non-monogamy is not wrong, you're not a mug, there are lots of people doing it, and it can and does work.
Have a hug. x