Hi Readybrek
You refer to your OH as "partner", does this mean you are not married to him? If this is the case, I would guess, and it is a guess because I am certainly not a lawyer, that you have no claim over his two children under the Hague Convention and he has no claim over your one child either. So if it were to all go wrong, you would go home with your one child (if you had to leave the country) and he would do whatever with his two.
As for would you get deported, you should be okay to stay in this country for as long as your visa is valid. You say you are on his visa, but surely your passport has a visa stamped in it, so whilst you did come in off the back of your partners visa, you do now have your own.
So, are you married or are you partners?