Key question: does your Chem II class include any organic or biochem? Or is it strictly Inorganic Chem II? I'm in Inorganic II right now, and I have to say, it wouldn't have mattered which other science I was taking (if I hadn't finished them already) at the same time as Chem II. However, when I was in microbiology, I was wishing I had some organic background, because there *can* be (depending on your teacher) places in micro where a background in organic or biochem would make some concepts easier. So if your Chem II has organic/biochem, you might want to take it first and then take microbiology.
Having said that, and as a veteran of taking multiple sciences each semester, I must say that you need to be able to keep yourself centered, and focused and able to go to "your happy place" when you need to.

Having an A&P and Chem exam on the same day is NOT FUN!
Also, I noticed you're contemplating taking Chem II in the summer, which is what I am doing. I love chem, and really wish I had more time, but it's a very intense experience no matter how you look at it. I would *not* even consider taking another science during the same summer session as Chem II, unless your summer sessions are unusually long. Just my 2 cents, of course.
Hope this helps.