Hey there,
Is your new girlfriend also polyamorous? Is she currently dating others as well as you? To some extent, it's normal to get a bit caught up in a new person and to want to spend lots of time getting to know them and exploring your connection, but the thing is, you are not single. You have an existing commitment to your wife, and your new partner needs to be understanding of that. It's your job as the hinge-person to find the balance. Dating when already in a relationship is really quite different (at least in my experience) to dating when single. You can't let yourself get too carried away. Factor in that you and your wife (and possibly your girlfriend) are also extremely new to this, and you have even more reason to take things slowly and keep everyone's expectations low.
The first thing you need to know is why you and your wife want to open your relationship. Obviously some aspects of non-monogamy appeal to you, and obviously you guys must have talked this through with each other and made that decision together, but it's good to be really clear. Are you both seeking the same kind of experience? Are you both going into this for your own reasons? Are you both equally keen to do this, or is one of you more 'meh' then 'yay'? It's okay if your motivations are different, but you need to understand your wife's reasons as much as your own. If it's to make up for something lacking between you and her, then it's best to work on that before adding others into the mix. If it's about sexual variety for one of you, and about forming romantic connections for the other, then you need to be mindful that those things are different and each of you will take a different path to adjusting to your partner striking out with a new person. If you and your wife are in conflict about what kind of open relationship you want to practise, this is something to resolve immediately. Opening up when already in an existing relationship is harder because you both need to be on the same page about this from the get-go.
For me, I find it much easier when my partner is just developing a sexual friendship type bond with someone than when she's all caught up in the romance. In the former case, I find it easier to be happy for her. In the latter case, I find it easier to feel insecure and like my place in her life is in doubt. I am a firm believer in the fact that you cannot control when you feel love and when you don't though, so I would never try to say to my partner that she can only have relationships of a certain type. However, knowing my own responses and feelings and insecurities can certainly help us BOTH to work together to get through difficult periods. If your wife is similar, then what she needs is for you to be confident and reassuring of your love and commitment - and you can only do this if you know how she feels, and she knows in a sense, what would make her feel better and can ask for it. It sounds like she's telling you that she's missing your presence in her life. If you guys haven't been having much quality date-time together, then carve some out. Show her that you want to date her just like the new girlfriend. Don't just assume that because she has the ring on her finger and gets to wake up next to you that her place in your life is secure.
As for your girlfriend, you need to be realistic about what you can and cannot offer her at this stage. On this forum you'll hear many different examples about how people organise their relationships. Some people practise solo-polyamory, and don't live with their partners. Some people have one 'primary' relationship within which to form long-term life entanglements, and then one or more other relationships that are not as closely tied together. Some people desire equal partnerships all around, and are prepared to either share one home and create a family unit with all their lovers, or split their time across multiple households in order to make things work. Your girlfriend needs to know what kind of open relationship you want. Note: this is why it's important that you and wife are in agreement and wanting the same thing. You need to be able to look girlfriend in the eye and tell her that this is what YOU want, not this is what my wife insists on. As the hinge, don't be coming at discussions with your girlfriend from the standpoint of 'I'd love to see you but wife is feeling down today, maybe next week'. It should be 'I'd like to give wife some support so this week doesn't work for me, maybe next week.' Or better yet, simply 'I've got a lot on this week, next week is better'. That being said, once you have fixed a date with girlfriend, *don't* just cancel it at the last minute if wife is feeling rough. Plan it in advance with wife, and make sure you have her support *before* arranging a date. That way she has time to prepare mentally, ask for any before- or after-care that she needs, and you are not messing girlfriend around.
It's not easy being in your girlfriend's shoes, especially if she's not actually polyamorous herself. All relationships start off insecure and jittery, and given that managing multiple relationships is new to you, I'm not surprised she's also feeling a bit insecure and possessive of your time. It's up to you to set the boundaries though. I think it takes a lot of self-awareness and confidence to feel an intense emotion like love and just let go and feel it when you don't have a clear road-map laid out. If she's coming at this off the back of mostly monogamous experiences, that might be daunting, and if the type of open relationship you and your wife have agreed on is not one where she could reasonably expect to become your life partner/co-primary, it may not actually be something she even wants. At some point, you have to consider whether you can actually offer her what she wants. Personally I would not date someone who identified as monogamous, or who lacked (but yearned for) a primary partner of their own, as I know that I couldn't offer them that.
You don't say how often you have been seeing your girlfriend, and in any case, there's no 'one-size-fits-all' number of times per week/month that is excessive or not enough - there is only what works for each group of individuals. I think it's worth investigating with wife what her expectations are. Find out how much time she needs to spend with you to feel connected. Would it help if more of that time was 'quality time' vs 'spending time in the same house time'? Would having more intimate time with you, either before or after a date, help her? Would she rather have some space? Keep the conversation focused on you and her and your shared relationship, not your girlfriend. There is a huge difference between 'I only want you to see her once a week' and 'I'd like some quality time with you at least six times a week'. The first is a mandate, that doesn't get to the root of the issue (wanting to see you more) and the second is a useful guide that allows room for compromise. Perhaps you can spend time with her AND girlfriend doing something fun, and that would count as quality time for both. Or perhaps you can make sure wife gets some attention in the early evening before you go out and see girlfriend.
Don't be surprised (or angry) if you find that when wife gets a regular partner of her own to date, a lot of this goes away. Speaking personally, having a lover of my own and realising that it didn't change the way I felt about my partner did more to click things into place than any amount of talking and reassuring that I received in the run up. Sometimes that's just the way these things work. Be patient, have compassion for both of them (and yourself), and just do your best. It's all anyone can ask of you at the end of the day.