Shared parental leave

I work for the NHS and my wife works for a small company. I’m currently 21+4 weeks with our first baby. We had planned for her to take the equivalent of paternity leave and for me to take about 9 months maternity leave before going back to work. But the closer we get to baby’s arrival the more certain I am that I don’t want to go back to the NHS. This would mean I only get SMP because any enhanced pay has to be given back unless you go back to them for 3 months. Luckily my wife is really supportive of this, and because of my qualifications I can get some part time work once baby is about 6 months old so that finances won’t be in dire straits. Does anyone know whether this means that we would be entitled to my wife’s company’s maternity benefits if I’m not making use of enhanced maternity pay from the NHS? I’ve not really understood the differences with shared parental leave vs maternity and paternity pay, and obviously we’re both mothers rather than either of us being a father. Any suggestions or advice massively gratefully received!