Oh lord. OP, there is absolutely no way I would turn this down. These are the trips where memories of a lifetime are made! Your children will remember and cherish this trip forever. And bless your mum for offering to do this.
These trips cost an arm and a leg and no, I’m sorry, but if no adult on your DP’s side can afford this then you go, with your children. End of. I cannot believe you are considering not taking your children for a child (bluntly) who is not related to your mum.
And if your last update is correct (you won’t have a relationship to come back to), please think long and hard before progressing this relationship. Your DP has given you a very nasty ultimatum that is based in control/ jealousy.
I take my children away (just the 4 of us) on trips that my DP can not afford with his children. I make no apology for it. And if he ever gave me an ultimatum? He wouldn’t have a relationship to make that ultimatum within.
I would also think long and hard before selling your house to move in with this man. Have you taken any legal advice before taking this step?
Have you pre agreed / signed a co-habitting agreement before taking this step? Have you both done full financial disclosure to one another?
Let me make it clear, your negotiation power is at it strongest now. Whilst you are in your own home and financially stable and independent from this man. Do you know for example if he has any borrowing against his house? Is he financially stable and if you split up, can he afford to give you his equity back? (If he cant afford $2k for the trip of a lifetime for his son then I am hazarding the answer is no).
If you sell your house and plow your equity into doing an extension on his house. His house will increase in value. If you split up, on top of your equity, what % of the additional value on the property is yours? Given it is 100% of your equity that has increased the value? Have you discussed these terms? With lawyers? Has he agreed to them and signed anything?
I’m sorry but you seem wholly naive. And I cannot believe that you are selling your house to live with a man and a child whom you have never done this with. You may think the children will be fine but the reality of fulltime blending is far more complex than you think. How do your children feel about their home being sold?
If I was ever to live with my DP, iron clad agreements would be signed. One of us would rent our home to live with the other. And if after a period of 6-18 months everyone had adjusted, we would maybe look to get a property together. But there is no chance I would ever sell my house to move in with my partner. My home (and the equity) is my stability and future for my children. And they come first.