There is no issue I believe - several children at the childcare center my two go to do this (which is an approved 4 year old kinder provider), some kinder days at a community kinder some Childcare days. You just pay normal CC fees, although most places the fee is not as much for the kinder rooms (ours is I think 5 a day less for kinder rooms).

I would see it as a plus - if your childcare center offers a kinder program, it has to follow the same curriculum as community kinders - so essentially he will get three days of kinder. (If only doing childcare based kinder - they like to have attendance for at least two days - but as he is doing a kinder program elsewhere then no issues)

Based on what my 4 year old does at CC based kinder and what some of her friends do at community based kinder, there appears to be little difference - so personally I wouldn't choose to move to community kinder just based on content - but it sounds like you have other good reasons to do it anyway. I do have a friend who does exactly what you are suggesting two days in community and one in childcare and she has said she wishes she hadn't though because finds the pick up and drop off for kinder very stressful to fit in with work and traffic - childcare you pick up and drop off when you pick up and drop off but kinder has set times and she finds it hard with work and given her greater understanding of childcare based kinder thinks for her second child she wouldn't opt for community while working (plus she has to drop off her second child at the childcare center anyway) - might not apply to you but thought was worth mentioning.