Kathryn
I think that the best option for you is to call Northern Rock and see what they can suggest that you do. You are not "asset" insolvent, given the equity in your property, but are "cash" insolvent as you have insufficient money to pay your debts as they fall due.
If you are intending on selling the property at some stage, presumably then you will want to clear your debts from the sale proceeds, so why not invite Northern Rock to take some security against your property in return for lower repayments? You really have nothing to lose. Why not remortgage the property, as you have sufficient disposable income to cover the repayments (which would be lower than your are currently paying your creditors) and this would not affect your children's share.
Regards, Melanie Giles, Insolvency Practitioner for over 20 years.
For further details contact me at
http://www.melaniegiles.com and view my IVA blog at:
http://melaniegiles.blogs.iva.co.uk