Hi gt and welcome to the forum
I think that payments of £661 per month are very tight, but would need to see a summary of all of your expenditure to advise further.
Moving in with your partner seems an excellent idea, especially as you both have children, and you will be able to share some of the costs. If I were you, I would sort this out before entering into an IVA, as you will need to price out all of the new costs such as rent, council tax and water rates, light and heat, and insurances, as well as your general shopping and household budget. Your partner's income will also need to be confirmed to ensure that you are paying a fair share of the new combined expenditure.
Bankruptcy is also an option, but only you can decide if it provides a better way of dealing with your debts. This really depends upon how bothered you are about repaying any of the money you owe, as it is rare to return anything to creditors under such proceedings as the costs are quite high. And as you point out if you have equity in your property this will vest in the bankruptcy trustee.
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