im 95% sure your solicitor will advise you to stay put. Once you leave the property you will struggle to get your ex out and you will remain responsible for the mortgage payments (if your wife defaults) whilst she continues to reside there upto the youngest child leaving full time education. This is along with your own rent. I would encourage discussion that either party buy the other out, or sell the home and split the equity as you agree, allowing both parties to move on. So far as I know, you would be unable to obtain another mortgage whilst tied into the old one so you’d be tied to renting long term. If I were you I’d stay put and ensure that child contact arrangements, financial split and anything else you have questions about are all agreed as part of your divorce settlement.
Do not leave your house or listen to your wife. If she wants to clear off with her bloke then let her. Once you move out she will change the locks and you won’t be able to get back on.
You can’t pay 2 sets of bills because your wife is harassing to move out. When you go to solicitors you need to get it all on writing how much all this will cost. Letters cost £250. Emails around £15 so it will be costly once the legal team knows you have property . They couldn’t care less of you can afford to pay them because they can collect their fees once the property is sold.