This is never an easy decision to make, Monkey Foot.
If you stay it is likely that Mum will attempt to have you forced out - she can apply for an occupation order which will bar you from entering the house and is often accompanied by a non-molestation order. Neither is easy to deal with and both can cause problems later down the line if you find it necessary to apply for a child arrangements order.
If you leave it can also cause problems; you will lose your bargaining position and it can be presented as you abandoning your children, you will hand the Mother de facto custody, you will become liable for child and spousal support, you will lose your home and you will lose any possessions you leave behind. If you want to retrieve anything you will have to negotiate a time with the mother or with her solicitors and you may have to provide proof of ownership. You will also leave room for your wife to move her new man. Is this an environment in which you want to leave your children?
On balance you should stay - since it is your wife who wishes to end the relationship it should be her who moves out. Have you considered
mediation or counselling through Relate? Ideally you need to resolve these issues before progressing with the divorce.
Discuss your options with your solicitor, but be proactive and take any steps you need to take in order to protect your children and your relationship with them.