Hello and welcome along.
Like as not your credit is already affected by having a reduced payment on the first credit card so I wouldn't worry unduly about making it any worse.
Seems to me that there are 2 ways to approach the other cards, you can try and do what you have already done with the first one which costs you nothing directly, or you can approach someone to look at a temporary DMP for you whilst you sort yourself out. You could look at a non fee payer such as CCCS or a fee payer, the choice must be yours. When the house sells and the equity issue is sorted out then you can pay the debts off in full.
For the meantime though, it sounds as if getting you and the children out of an unhealthy environment is top of the list and rightly so, although the debts are important and need sorting, they are not as important as your health and the wellbeing of you and the children. You may wish to visit
www.iva.com and take advice from a professional directly, at the very least all initial contact should be at no charge to yourself.
I wish you all the best and do let us know how you get on.
Regards.