Does uterus support bladder muscles that can relax if uterus is removed and result in urine retention and uti?

No: The uterus is supported by 3 independent ligaments as the it sits behind the bladder. When the uterus is removed the bladder is able to support itself independently. Patients who have previously had C/sections have had the bladder dissected off of the uterus and replaced post delivery. This can cause scarring(adhesions) of the bladder to the uterus with frequent UTI's & retention.

Not exactly: If someone has their uterus removed then some women may experience mild prolapse of the bladder (cystocele). Some women with a cystocele may experience urinary retention or bladder infections. Have an Obgyn do an exam to determine if a cystocele is present. This can occur in women without a hysterectomy as well.