My little girl has just turned one and is also crying whenver I put her down, mostly just after a nappy change cause she knows that I have to leave her sight to wash my hands! I'm still looking for a solution to that one....but if I need the loo (as you do!) I find that I can usually enlist the help of my 4 yr old to "entertain" her while I go. Showers are out of the question until my hubby gets home from work, unless I try washing one-handed (very tricky to wash hair!).
On the subject of your girl's strong will - my sister always had amazing tantrums when we were growing up and never did anything she didn't want to do...she is now a National HR manager and still never does what she doesn't want to! I guess what I'm trying to say is that a strong willed child is a blessing in a lot of ways - she will never be talked into anything she isn't sure of. Light at the end of the tunnel?
Best wishes in finding what is right for you and yours while you go through this 'stage'...it will pass, I promise!!