Thanks for finding and reporting all these bugs!
I've released version 5.7 this morning which should fix the following:
- You can now invite girls over whilst a live-in partner is present.
- Fixed a bunch of bugs with the council carers & you should now be able to make love to them again.
- The doctors office should appear correctly as a date option for all girls.
- The care home matron should now be replaced correctly and this will also happen when loading a save if she's missing.
- Fixed the yoga bug.
I'm going to take a closer look at how girls move around when at the high weight stages, but 5.7 also includes a few improvements here too. I'll get the rest of your suggestions/feedback addressed soon.