Ok - another non-Dad here.

I think that it is absolutely your birth and you can choose anything you want for it and do deserve wonderful support from whoever is your support person.

Have you really discussed this in depth with your DH? Does he realise that you weren't satisfied with his performance last time and have you discussed ways that he could improve.

Does he get along really well with your Mum. I wouldn't want to see a situation where they went into competition as to who was the better support person so you got a little crowded out (as happened with a friend of mine - there were almost a punchup at 8cm dilation)

I'm not sure about cutting the cord as I have no strong feelings towards it generally but I really think that you need to calmly sit down with him and really talk about it without getting into who deserves to as each of you have perfectly valid reasons and you have to find a compromise.