Tammy, I'm dithering here. . .I feel like I should respond to your question because I work in the poetry publishing world (I'm a part-time editor at a London based literary magazine) plus I'm a "poet" myself, with a collection to be published in the US next year and, hopefully, distributed to some UK bookshops. But in another way I feel like I shouldn't respond to your query because I'm kinda jaded about the whole poetry publishing thing, and maybe you need someone more positive. Basically the distinguished magazines that publish poetry (London Review of Books, TLS, Poetry Review, Arete, The New Yorker, PN Review, Poetry London, Poetry Wales et al) accept no more than 1-2% of the submissions they receive. If a submission happens to contain "roses are red, violets are blue" type verse, or the kind of stuff that circulates the internet, they will literally throw it away upon reading the first two lines because (a) these mags are understaffed and (b) what they're looking for is work that reflects a familiarity with old and contemporary English-language poetry, and probably foreign poetry in translation, too. If what you write is more low-key, there is still probably a market for it, no doubt contained in the useful book that Miaou suggested, which lists practically all the periodicals that publish poetry.
If you've written a lot of poems and want to publish a book, then unfortunately you need to publish a lot of individual poems first, at least half of the poems contained in your collection. If you pursue this path, you have to expect (a) absolutely no money. Even when my work appeared in Poetry, the American mag where T.S. Eliot first published "Prufrock," I got something like $40 which was a mockery to the weeks I spent writing and revising that poem (b) absolutely no respect--no one cares if you've written or published a poem, and (c) loads of loads of rejection letters of which I, personally, have collected enough to build a replica of Mt Everest.
I'm know you've had a hard time of things, tammybear, so please forgive this less-than-sunny but HONEST explanation of the poetry world. I think there's more joy to be found in the writing and reading of poetry, than in the publishing. What I'd suggest is that you read loads of poetry, if you don't already, andif it's possible to get away from the kids one night a week, saytake a class, or join a local writing group, just to get some feedback on the poems you're writing. I don't mean to sound patronizing, promise. . .it's the same advice I give myself