If the break up was messy, they may feel angry towards you for upsetting their mum. They may think you prefer your new partner’s children to them. You will need to prioritise time with them to show them that this isn’t true. This will mean your new partner will have to understand this – in any case, she is always going to have to understand that your own children come first and support this.
If she doesn’t, it’s going to be difficult for you to maintain your commitment to your children and as you're trying to be the best dad you can be, you will have to think about whether or not this relationship is going to work.
Next: Will the reality match the fantasy?