Welcome to our forum.
Re (from maximus, Post #1):
"I would love to pleasure her with another man, and when she is not in the mood, pleasure and be pleasured by my significant other (Brother? ... appologies, I am still learning the language and there was not a definition for brother on the introduction glossary)"
Not sure there's an exact word for what you're looking for, although "brother-husband" is a maybe. Otherwise you'd just say "partner" or "male partner."
As to what to do about your current problem, your wife's seemingly lowered libido, the others are right in saying it's better to address that first on its own merits, rather than trying to "add another person to the equation to fix it." I know that's probably not what you want to hear; you're eager to start a polyamorous life, but she needs to be on board with that idea before it gets under way.
Since begging, nagging, asking, pleading, and romanticising have not worked, you're sort of left with the direct approach, which is to sit her down and say, "Look, I would like us to have more of a romantic life with each other. What can be done that would help you feel more in the mood for that?" Getting some couples counseling would probably also be a good idea, if you can do that.
As the others have mentioned, taking care of kids is a huge responsibility, and she may just be worn out. But asking her, directly, what's making her have less libido, is the most obvious way of finding out why she has this lack of interest.
CielDuMatin is right in pointing out that when you guys got married, you made promises to be monogamous to each other, so she's not wrong to want it to stay monogamous. On the other hand, I couldn't say why she seemed interested in a threesome, but not so much now. Again, the direct approach might be the way to go. Such as saying to her, "I know there was a time before we got married when you seemed to think a threesome might be of interest to you. What do you feel is different about now that a threesome no longer sounds good to you?"
She may come around about the poly thing if she reads up about it and gets more familiar with it. Franklin Veaux
has some good web pages about the subject. But first you need to get your marriage with her on solid ground without bringing up the poly stuff. It's probably the only way she'll eventually be willing to consider it (and of course I can't guarantee it even then).
You're not 100% happy in the marriage right now, and in all likelihood, neither is she. She is probably hoping you'll do something about that, before bringing up any threesomes or poly propositions. That's what I'm guessing, anyway.
Hope this has been of some help.