I am absolutely shocked at the way the nursery has dealt with this.
It is the responsibility of the nursery and its staff to care for all of the children in their care - including your ds's.
You have explained to them clearly that ds is a biter and told them ways of dealing with it - though to be honest they should have their own ideas on this.
It is common practice in this kind of situation to have a staff member (Preferably DS's keyworker - though obviously this isn't always possible) to shadow him during the day and intervene where necessary. Do you know what their behavioural policy is like? (Am not saying he has behavioural issues by the way lots of children are biters - the nursery staff should have clear ideas and training on how to deal with this)
To be honest I think the main problem here is how the nursery have reacted to the situation.
I have been working in nurseries for the past 18 years and have been a nursery owner/manager for the past 11. I understand how difficult it is to deal with parents who obviously are upset that their child has been hurt BUT the nursery manager/senior staff should know how to deal calmly and professionaly with all involved.
I would have expected my staff to (politely) apologise profusely for this happening whilst the child was in our care and assure the parent that we would be closely monitoring the situation and doing all we can to make sure this never happens again - end of.
The nursery staff should not have got involved in any further discussion with the parents regarding your son and when he will be at nursery and they should have a clear confidentiality policy (Signed by all staff) preventing them from doing so.
It is extremely unproffesional of ds's keyworker to ring you and tell you what the other mum has been saying (again confidentiality issues). Is this keyworker a senior member of staff - If not I would highly recommend that you speak to one of them asap and ask them to sort out the situation, explaining to them in detail how your keyworker has been dealing with it.
Finally somebody needs to make it clear to the other parent that while they understand she is upset about the incident there is no way that they can stop your child from attending because of this.
If she feels that is unreasonable and does not want her DD there with your son then that is her problem, and then up to her to sort it out and arrange alternative care.
If they ask you not to bring him you might want to bring up "equal opportunities" and "discrimination"
(I take it you have a signed contract with them - check what this says about notice periods and asking a child to leave).
I do not understand why the nursery feel you need to go and have a chat with them about the whole thing - you have already spoke to them about his biting - the rest is their responsibilty but it may be worth asking them what think they can do to help him through this.
I have taken my "nursery hat" off now and will go back to being a mum.
My eldest ds was a biter and I know exactly how embarassing it can be when they are going through this phase. You are doing exactly the right thing though by teaching him this is wrong and moving him away from the situation - there is nothing more that you can do.
He is not being naughty at all - He is far too young to understand. Unfotunatley there are many reasons why young children bite and teething is just one of them.
The other parent is being completely OTT about this and I hope that in time she realises this.