If there's one piece of advice I want you to keep in mind in the heat of a salary negotiation, it's to remember: It's not about you (personally).
Seems crazy, right?
But, as a strategy for success, remember that it's not about you. Don't take any part of this conversation personally; that will only make you defensive.
For example, providing details about your personal life as a reason you need a particular salary or raise is highly unlikely to convince an employer that they should increase your salary. After all, most people experience raising rents, high childcare costs, the need to save more money, etc. These are, unfortunately, not reasons to require you be given a raise or offered a particular salary.
This is not to say you should accept a salary lower than what you believe you are worth, and what aligns your expectations. It means you need to tie your ideal number to your achievements and professional outcomes you can deliver. Not the fact that you have expenses. And, it could mean that certain employers, industries, or functional roles are not right for you if the market will simply not bear the salary level you're looking for.
The more objective and formulaic you can keep the conversation (i.e., "I have achieved X, Y, and Z; I will deliver A, B, and C), the fewer opportunities the employer has to simply dismiss your case.
Negotiation is often about finding ways to keep the conversation going to create opportunities for both parties to get more of what they want. Making it and taking it personal results in the opposite. So, try your best to avoid this tactic whenever possible.