Not that it's much comfort, but your experience is not uncommon. In fact there's a somewhat dated and vague term, lesbian bed death to describe the phenomenon in same sex relationships, and the heterocentric term "sexless marriage" is often used to label people who find themselves in committed, loving, long term relationships where their sexual needs are just not getting met.
Without diminishing the frustration of your situation I want to start by highlighting some of the positive things you've got going on. Figuring out a way to share a life, a home, and a family isn't easy. If you and your partner are already doing these things then you know you can work together.
When sex doesn't work in a relationship, it's so easy to feel like a failure. Because there isn't a lot of honest talk about sex in public it's easy to feel like everyone else is doing it better, everyone else manages to figure it out, and you are the only ones who are stuck. It's reasonable if either (or both) of you are feeling that way, but I want to suggest that you might give yourselves individually and even as a family a break too and remember that you have a lot of strengths which can help you figure out this situation too.
My short answer to your question is to say that this would be an ideal time to do consider getting support from a counselor or therapist. Neither of you want to end the relationship and there are many aspects of your family life that you are satisfied with, but something is missing and you want to figure out what it is precisely, and then how to get it. Doing this on your own, and even by talking with family and/or friends can be difficult to impossible. Negotiating relationships is hard. And it's made more difficult by all the social pressures and expectations we bring to the relationship. To also have a child and a family together adds more pressure. All of this can make it feel almost impossible to untangle expectation, responsibility, and guilt enough to get to your own desires, hopes, and dreams. And you need to get there.
A good therapist or counselor can offer space and support for both of you to get a bit clearer on what it is that you want. And they can help the two of you explore what that looks like in a safer way than doing it on your own, at home, in between the tasks of daily living. Obviously this is just my opinion, but I find topics like monogamy so fraught, that having a third party there is almost essential. I think there's a myth that these issues are only a challenge for people in heterosexual relationships. In my experience that's not true.
Would you both be open to seeing a therapist? If the answer is yes the next step is to find someone good. Therapists come to their work with their own baggage which includes homophobia, transphobia, and heteronormative ideas about compulsory monogamy. So I would want to make sure you got a referral to someone who a) isn't going to be putting their baggage about sexual orientation and identity on to you and b) won't be freaked out by talk of opening up the relationship.
I have a longer answer too, which is below if you're interested.
If you don't want to start with therapy right away but would like to find a way to structure conversations with your partner about possible ways to reconfigure the relationship you could start by reading together. You don't need to read it with any particular intention or plan in place. Consider it more of a book club for the two of you. I haven't had a chance to read it yet but I've heard lots of good things about Tristan Taormino's book Opening Up. If you are already at a point where you can both talk about this without one or the other getting defensive or shutting down, then it might spark some useful conversations.
It is possible to have a family and construct a sexual life that involves having sex with others. But it takes work and clear communication and commitment. Some people would say that it's better not to go down that road because it is more likely to lead to the end of the relationship. And for some people this is undoubtedly true. But your relationship is yours. And no one else can say for certain the 'right' way for you to be in that relationship. Also I can't help but think that those who say you shouldn't even think about it say so in part because they believe that we 'should' be monogamous, we 'should' sacrifice, and that we can't have it all. My response would be to say that even people who do manage to be in a family unit and have sex sometimes outside of it, aren't 'having it all.'
What a new configuration would look like depends on so many things, and it must be guided by the two of you. You may not be talking about opening up your relationship to other people, it might just be about getting to have casual sex with others. And maybe you each put requirements around the sex (common things include not having sex with anyone in your immediate circle of friends, not developing anything more than a casual relationship with the people you have sex with, scheduling a particular day or days when it's okay for one of you to go out, the options are almost limitless). This again is where a counselor or therapist can come in handy since part of what you need to do is figure out what it is you want. It doesn't sound like you actually want to change the structure or dynamic of your family or even the relationship you have with each other. I would suggest that it's possible to get what you want here but it won't be easy. Because life isn't easy.
One thing that I wonder about based on your email is if you and your partner have a sense of what the ideal situation would be. Would you prefer if you felt as sexually attracted to your partner now as you did at the beginning of your relationship? Would you prefer to figure out a way to make monogamy work? Or do you, like many people, simply like to have sex with more than one person, and would you prefer to find a way to bring that back into your life?
It sounds like you both are clear that you don't want to do something that will put your family in jeopardy of breaking up. Having a shared value and goal like this is excellent. Since you both know that you want to make your family and relationship work, that seems like a good boundary to be mindful of. So, for example, you might agree that if you're going to explore the possibility of opening your sexual relationship up, either of you has the right to call for a time out at any time if you are feeling threatened or unhappy to the point where you are questioning the future of the relationship. If you're going to explore this it is crucial that you each are aware of your limits and that you are able to communicate where they are and act on the information you share.
Finally I want to acknowledge that doing all this as a parent is going to be challenging in ways that have much more to do with social expectations than with the daily work of parenting. There's so much social pressure put on parents and I have no doubt that if you start having conversations with friends about this people will be judgmental because you have a child. As a parent you do sacrifice and compromise for the sake of your child. All good parents do that. Actually all grown ups do that simply to be in the world with each other. But that doesn't mean you have to (or should) sacrifice a big part of who you are, your sexuality.
If you do decide to open up the sexual part of your relationship you'll likely encounter some judgment from people without kids as well. The iconic parent is not one who is out getting laid. Of course lots of parents are, but they do it in secret. You'll be confronted with people's stereotypes of what a parent is in this realm just as you are when you're out on the street with your child and people make other kinds of assumptions about you, your child, and your family. I wish this weren't so. And I'm not saying this to discourage you from pursing these conversations with your partner. I'm saying it just to give you some support around the fact that to get what you want you'll likely be confronted with a lot of people's stereotypes and expectations of who you are in a way that you might not have before having a kid. But being a great parent AND taking care of yourself are not incompatible. And having a healthy and satisfying sex life and sexual expression is absolutely part of taking care of yourself.
If you have any questions about what I've written or want clarification please feel free to let me know.