kids accounts depend on how it's set up - if it's an account you may have access to and it's deemed you may be "hiding" money, then it may be deemed an asset - always best to show the details and have it up front so the person assessing can see what's going on. money in kids accounts is normally theirs, so doesn't count - but if it's an every day access account with a large sum in it that you have access to, it might be questioned. if you invested money from the sale of the house and put it in trust for the kids when they are 18 or something, it would generally be deemed to not be your asset
money from sale of house - if you intend to purchase again within 12 months, it may be treated differently, but essentially any money sitting in a bank account is deemed an asset and can count towards the asset test for a payment. if there is money in an account, interest from it will also be deemed an income

money like this impacts any income support payment (parenting, newstart, carers, disability etc) and is assessed by c'link
the impact it has on ftb is determined by how the ATO treats the money.