How to Calm Separation Anxiety in My 9 Month Old

Your child is scared in your friends house.
So hold her while she naps - in a sling if necessary.
Your mental condition is something you are going to have to live with and deal with always.
It's not an excuse or a crutch - don't let it become one.
Your child did not ask to be born.
You have a responsibility to see her needs and sometimes this will be in conflict with your own.
If you've told your doctor what happens to your child on these visits, I'm sure he is NOT in favor of your child suffering for it.
Hire a sitter for your child so you can visit without bringing her or never let your child come into contact with the toddler while you are there.
Look for a schizophrenic support group and try to widen your circle of friends.

I never tried to get my kids to nap in strange houses. My daughter wouldn't even nap at my mom's house. It just caused her too much anxiety.

We planned our outings around the nap schedule.

I wish I had other advice, but some kids (like adults) just prefer their own beds.

Is this the same friend whose daughter pushes her down and slams her head against the ground? I'd be afraid to sleep in that house too.

ADDED at the top after the SWH addition:
Kaydon, find a moms' group at a time of day that works in your child's nap schedule. You need to get out, yes! But this friend's house is NOT the place to do it. Contact your local hospital chain (they often run new-moms' groups) or find a church that hosts groups or a community center that hosts them. I'm talking here NOTt about a "mothers' day out" where you leave the baby, but a moms' discussion group where you all sit with your infants and chat. You do need to get out, but can you see how this friend's house is not the place to do it? The stress of worrying about your child's safety there is only going to make your own condition worse! There are groups out there if you look. And ensure that your husband or significant other is looking after the baby and letting you get out and see people at other times. Good luck!

Kaydon, is this the same friend you mention in your other post today? The one with the toddler who pushes over your baby? Can you see the connection? Your baby knows this is not a safe place for her.

Your child is only nine months old. Please read up on stages of child development so you have more realistic and age-appropriate expectations for her behaviors.

She does not do it at your mom's probably because she knows your mom very well and there also is not a toddler there of whom she is physically afraid. Please recognize that your friend's house simply scares her to death and do not try to seek "solutions" to it -- just do not take her there. Your baby is too young for you to be able to fix this or "help her through it." She is pure reaction and pure emotion -- nothing will fix this fear other than removing the cause of it.

Leave the baby at your mom's and go visit the friend on your own without the baby along!

I was always a "make it work" kind of mom at this age. If we were not in our home, I'd hold or rock my kiddos to sleep for their nap. Whereas at home, plop, just lay em down.
A special lovey or reminder of home could help. Maybe soft music, etc.
sometimes just avoiding a nap-time visit was helpful too. Visiting, instead, right after they wake up or doing the "car nap" on the way over.:)

I just read the other post. Now you know why she screams and is unhappy. She does not like to be pushed down and hurt. Put your baby first. Make another friendship.