I recently went through the experience of linking each of my two blogs to its own Twitter page. I got some good help here; but finally, I needed to do it on my own, by
1) Set the two Twitter pages up on separate browsers (like many people, I use more than one browser) and
2) Quit the use of Publicize.
I link the two blogs to both Twitter and Facebook. Facebook was already a problem with Publicize, as Facebook will only allow one blog, linked actually by RSS. If you Publicize a second blog, Facebook just kicks out the original blog.
So, now I need to use the Facebook and Twitter share buttons on my blog pages, doing it manually. But, this had a couple of unexpected benefits:
1) For Twitter, you actually get to write a Twitter post, instead of allowing Twitter to do its own brief text. So, you choose the text.
2) For Facebook, if you have included some number of graphics in your WordPress post, using the Facebook share button allows you to choose which of the graphics will show up as a thumbnail at Facebook. When you use Publicize, Facebook would pick the graphic, often the last one in your WordPress post, and maybe not the one you would choose for yourself.
The benefits above are just as true if you have one blog as if you have more than one. You get to tailor what gors to your social media.
So, these are reasons to abandon Publicize, put the Share buttons on your blog or blogs, and do it yourself manually.