Frivalous spending does sound like the root cause and maybe it's a good thing that you're looking at this now when you're 'only' in £15k of credit card and 'only' on the second round of getting into trouble and wanting to borrow more to shift your debt around but kidding yourself that you're clearing it.
Plenty of people don't reach crisis desperation point until they're £40/50k in debt, so well done if you manage to break the cycle now.
IVAs are like 'bankruptcy lite' and not really a solution for people with room to cut back, which it really looks like you do have.
Your mortgage is quite low, but you are paying a lot on cars - do you need 2 cars, can either of you cycle or use public transport? Do you need cars on finance, or can you buy cheaper ones outright?
£80 pm for phones is loads, stop renewing expensive contracts with 'free' phones, go sim only and keep your old phone for more than 2 years.
Utilities is quite a lot, are you on the best deal and do you try to save energy?
Are you taking advantage of childcare help like tax free childcare etc?
Sounds like you need to start from scratch with:
www.moneysavingexpert.com/family/money-help/
Good luck, it takes a huge change in mindset to go from being a spender for a saver, but you have a reasonable income and a smallish mortgage, so you should be quite comfortable, not struggling and getting into debt.
How much do you spend on food and drink out of the house - this can be a huge cost, so one to look at by taking your own lunch and coffee to work from home.