It's a poem; you can say anything you want, and you can make the lines however long you'd like. Whether or not the end result will be perceived as inspirational or corny is another matter.
While it's true the invitation will need to contain certain information, I disagree with your assertion that you must "use certain keywords, like delivery." There are many ways to get the point across, without using the word delivery. For example:
The newborn twins will first be seen
On January seventeen
As for the varying lengths of the lines, I prefer consistency in that regard, particularly when there is rhyme involved. However, that's just my personal preference, and I don't think you'd be the first poet to end a poem with lines that stretch a little longer than the others. However, if you're trying to keep the poem consistent, and those lines are longer simply because you're forcing a rhyme, then I'd suggest working at it until your poem flowed a little more evenly. Just like in any other form of writing, the difference between a mediocre work and a very good work is often found in the amount of effort spent polishing and revising.
May God bless them ever after
Filled with hope and love and laughter