As part of any negotiations and financial relief proceedings you will both need to provide each other full and frank financial disclosure and he will need to demonstrate that he is maximising his income. If he cannot earn more than £35,000 then this is the figure that the court will consider when deciding on your application for financial relief.
As a starting point, on a salary of £35k, his child maintenance liability will be in the region of £77 per week and this is the enforceable amount you can seek through the Child Maintenance Service and no court application is required - only an application to the CMS who will deal with this.
In relation to spousal maintenance to cover your reasonable needs - this will depend on you maximising your income and it would be possible to seek for him to cover any shortfall, but the simply fact is if he cannot afford it, the court will not make such an order and other options will need to be considered such as further dividing the available assets to take into account your needs.
In the event that you remaining in the home, if you cannot afford to maintain the outgoings on the home and he cannot afford to assist, then the court may decide it must be sold and equity divided in equitable shares between you.
His partner's finances can be taken into account as it would be expected that his needs will be lower as they should be sharing outgoings between them.
In relation to the child arrangement issues, it is not appropriate that he has his new partner be involved in the school runs and if you do not consent to overnight stays for welfare reasons, then you can object to this.
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