Musgrove Park Hospital in Taunton, which will care for many of the women who would have given birth in Yeovil, was declared "inadequate" in a report by health watchdog Care Quality Commission last year.
Patients have previously described the hospital's maternity service as "traumatic, super hot and overcrowded".
Mr Dance told the BBC he had seen an increase in women planning to have home births as they would not feel safe at Musgrove.
"If something goes wrong – where are they going to go? Because having to get in a car to go 45 minutes to Taunton might be too long," he said.
A spokesperson for the NHS Trust thanked Mr Dance for securing the debate, adding: "We had a discussion with MPs this morning to talk through and respond to their concerns and questions, and we will continue to do this."
They also said everyone had been "given the opportunity to speak to their midwife about their choices for place of birth", and urged expectant parents to speak to the Trust, Somerset Maternity and Neonatal Voices Partnership about their concerns.
