We can afford to pay just over the minimum payment
Good. Put things on minimum and aim to change behaviour - no using credit cards ever again.
When is the family wedding - is there time to save up for the cost? See how cheaply you can do it - work out realistic costs for travel and accommodation (staying with other family, low cost hotel, only going for some of the wedding not all of it). Other people need to recognise that you are broke and can't be spending out a lot.
Emergencies happen, so you need to create a buffer. Around £1000 is a starting buffer, which may sound daunting right now but can be achieved. Look at ways to increase income and reduce outgoings.
It is very hard to give any figure for what a family should be spending. It will vary a lot. Your children are young so you have cost of things like nappies but don't have much in terms of cost of activities/outings as at their age they are happy to go to the park, woods, playground, toddler group, a train ride (they usually travel free), going on a bus (their travel is usually free). Meeting up with friends.
I want to be able to take them to Disneyland, that is my dream.
Setting a goal is good. Not sure that one is realistic right now but as a long term goal it's fine... you just need to realise that it is several years down the road. For now you want to set small goals, so you can feel that you are achieving something.
Goal 1: Having a roof over your head, food in your belly, electric - gas - water - internet - all on, clothing and transport.
Goal 2: Current on all debt repayment plans... keeping the wolves from your door. The wolves are still circling but they are now trying to blow your door in and taking your possessions.
Goal 3: A starter emergency fund. Your grandparents saved for a rainy day... they knew it was going to rain. You know it will rain, you need to save for that. Tyre goes on the car, washing machine springs a leak, child throws their shoe in the pond, child cuts their siblings hair. Life happens... things happen which we often cover by going in to debt (using a credit card) which is a habit that you need to get out of, by having money.
Goal 4: Spend money... real money. Not tap the plastic card. Stick to a budget, allocate a certain amount of money and have it as CASH so you spend what you have, not spend more than what you have.
Good categories for using cash are: Clothes & Shoes, Food (especially things like lunch whilst out/at work) and drink - I was spending over £40 a month at Starbucks on coffee... when you stop using the phone app/card and start paying cash, you FEEL the cost of that coffee!