If your partner having multiple partners while you don't is an unacceptable outcome for you then you definitely ought to get clear with your partner on what you'll do about it (collectively) if that happens before you start inviting other partners.
From what I've seen (monogamous man in a very poly-friendly social environment) yes, this is an issue that comes up, and yes, it's an expression of partners' insecurities. (This isn't intended as a dismissal; people have insecurities and relationships need to deal with those insecurities somehow.) It strikes me as similar to the issues some people have with partners who are significantly more romatically/sexually experienced than they are. In some ways it's also similar to the issues some people have with spouses who out-earn them financially.
One poly married couple I know deals with this by the wife, who is far more socially adept, helping her husband find other partners.
One approach you might consider is asking whether there's anything extra your primary partner could provide during the periods when she's more connected than you are that would make you feel less "raw end."
I infer from your assumptions that you're straight, but if not you might find it easier to find male poly-compatible partners than female ones. (In my experience it's less that women have an easier time finding dates, and more that it's easier to find male dates.)
Man, imagine if Eliezer or some other big name wrote "Bi-hacking" and LessWrong became known for all the deliberate bisexuals.
Related article: Polyhacking
Note: This article was posted earlier for less than a day but accidentally deleted.
Although polyamory isn't one of the "official" topics of LW interest (human cognition, AI, probability, etc...), this is the only community I'm part of where I expect a sufficiently high number of members to have experience with it to give useful feedback.
If you go looking for advice or articles about polyamory on the internet, you mostly get stuff written by polyamorists that are happy with their decisions. Is this selection bias? Where are the people whose relationships (or social lives, out anything) got damaged or ruined by experimenting with Consensual Non-Monogamy?
I'm posting this hoping for feedback, negative AND positive, on experiences with polyamory. I considered putting this in an Open Thread, but it occurred to me that many other LW readers might be interested in whether polyamory has drawbacks they need to be aware of. If you have experience with CNM (including first-hand witnessing, which has the added bonus of not requiring you to out yourself while still participating in the dialogue), please comment with your overall impression and as much detail as you would like to include (I am also putting my experiences there rather than in this post). If you've seen multiple poly relationships, multiple comments would make tallying slightly easier. I will try to upvote people who feed me data, a la LW surveys. If there are sufficient comments, I will periodically go through them and post a rough ratio of good to bad experiences at the bottom of this article.
PSA: The Username account is available for use by any who wish to remain anonymous. The password is left as an exercise for the reader. Hat tip... Username.