LNL - This is a point where you need to separate out the emotional aspects from the business aspects. Talk with an attorney, find out what your rights are, and what H is likely to win (or not) if he goes to the courts. I would imagine your country is more friendly to mothers than some, but that is just a guess.
Then, once you know what your status is: - consider not fighting him on the things that he is likely to win in court anyway. - Stand firm on those things you are likely to win in court. - if he gets nasty, just refer him to your attorney - consider carefully where you want to live. If you have any real thoughts of returning to your country of origin, now may be the time. But I suppose it might be difficult to enforce the child support if you are in another country? Is there another part of the country you are in that you would prefer? - is the house a good investment or will it be a financial albatross around your neck? If you keep it, can you rent out a room?
Pretend your H has died, and left debts equaling his share of the equity, and insurance equal to his child support payments. What would you plan for your future in that case?
Also - make SURE you know the laws in your country regarding that inheritance. In the US, an inheritance is separate, even if you are married - but only if you KEEP it separate. If you deposit it in a joint account, or start using it to pay for community things, or use community money to maintain inherited property, I believe it then is considered a marital property. I know you must be really careful about it.
Knowledge is power. Sounds like you need more.
As for H spending the night - I think the trick now is to set your limits while not provoking unnecessary reaction from him. Ask yourself - will this get me closer to my goal (of getting what I want from H). I would suggest "oh, I'm so sorry, my sister will be here then so it wouldn't be possible for you to stay here. Too bad. We'll miss you". Instead of what I know you WANT to say
