You know, I will be completely honest and say that until I had DD I didn't believe separation anxiety could really be so bad a mom would take her kid into the bathroom with her, and I thought those moms must be exaggerating a little. Well.......
boy did I ever have to eat my words. My DS had ZERO separation anxiety, ever. He was like the anti-AP-poster child
(not that I left him in containers all day, but he would have probably happily done that - he was happy to be on his own from the very beginning for periods of time that were always way longer than other similar aged babies and toddlers, and would happily spend time with any friends or family who wanted to hold or play with him). Then, DD made her appearance. Same parenting values and methods. She did not like being held by anyone but me or DH for the first 6 months of her life. She had severe separation anxiety from about 6-12 months (and I became that mom who pees with her child on her lap because they scream when you put them on the floor at your feet
She screamed when I went from the dining room to the kitchen to put a dish in the sink. She screamed when DH tried to occupy her while I showered. I was totally knocked for a loop. I would always talk to her and reassure her that I would be right back, but she just didn't get it. So I'd do things as quickly as possible, and bring her with me everywhere. At least she would sleep alone for a couple hours at night before I went to sleep with her, so I could have some time to myself; otherwise, I would have gone insane.
The good news is, I just left her for the first time with DH and DS to get my hair cut and colored, and she did fine, no tears (she's 14 months old). The same day, she played in her room happily while I showered (all fo 7 minutes), and played outside with big bro and grandma for an hour while I worked inside. Sooo, it's happening, finally. And I'm so glad it's on her terms. Sure, I could have forced us apart, but at what cost? Not worth it to me. So yeah, agreeing with everyone, and giving you a glimmer of hope!