OK. Not only was I an inventory clerk, I also had this happen to me, and I won, getting ALL my deposit back.
Your inventory:
Firstly it has to be accurate and prepared specifically for YOU. A copy of the inventory for the previous tenants and not fully and specifically updated for your tenancy will be treated as if there were NO INVENTORY at all in the first place.
If you can show that this inventory was not prepared and updated for your specific tenancy it actually doesn't matter if you TRASHED the place, the LL can't prove condition, so the FULL deposit will be returned to you.
Basically If a LL states that something is new and is damaged, the onus is on them to produce receipts to prove the age/condition of the item. If they can't/won't do this, or if there is any room for doubt, they will not be able to charge any compensation.
There is also Fair Wear and Tear to be factored in. If you were there for a couple of years, you having children means that a much greater degree of FW&T must be factored into the condition at the end of the tenancy than if you were living there on your own.
If they are trying to charge you for cleaning, again you can state that the property was not cleaned professionally prior to your moving in and if you have photos to prove this, your LL has NO chance of taking money off you.
Basically, in the eyes of the law, the money that is deposited with the DPS is YOURS. For the LL to claim a penny of it, they have to prove beyond all shadow of a doubt that they are entitled to it. If they can't, then the money will come back to you.
DON'T agree to a penny of deduction. The inventory they gave you doesn't hold you to anything as it is not a fair and accurate representation of contents and condition for your tenancy.
You can take this to Tribunal, and you WILL win. Don't worry for a second, the LL can't take a penny off you if the inventory is not prepared accurately for you.
Call the Deposit scheme and ask them to explain what you need to do. IIRC, they will ask you to complete you a statutory declaration, there is a form, they will send it to you, you fill it out, have it witnessed in a solicitors and send it off.
It will take a few weeks, but if your inventory is not prepared for you, you have NOTHING to worry about.
Do NOT roll over and just accept this, you can and will win this if your inventory is as I suspect a photo copy. doesn't matter if you signed it or not.
I did, it still didn't count.