I would be slighlty more balanced.
Firstly the massage parlour - not nice, but possibly better than having an affair. I doubt he will do that when you are together!
Secondly the children. You do not say how old they are? What do they think about it? If it really will break your heart to leave them, then you need to think carefully about whether this is really what you want. Plenty of men would be happy to accept your children - but whether they can settle in the UK does depend a lot on how old they are.
Regarding money, if you have agreed an amount and he has agreed it with you, then that should be that, no need to argue. I am sure you will be able to find work and send plenty more money to them. But as well as that you will need to plan to save up for regular trips home.
All in all it does not sound ideal - full of risks of you making a mistake. There are plenty more men around!
Oh, and by the way, you are NOT too demanding. you are being honest and saying what you need, which is a million times better than not saying it!
Good luck - I am sure it is a horrible thing to go through.
Ian