UD, just wanted to add some words of support as I am in a similar situation - living with partner in a host EU country with two young children, and feeling dissatisfied and trapped. It sounds like a lot of your problems may have come with your change of role to SAHM (and SAH wife!) Having children is a major transition and if one loses one's work/public identity at the same time it is very hard. Add moving country onto that and, well, things are likely to have been extremely tough for anyone in that situation. So try not to beat yourself up about it.
I also understand you taking things out on your partner too, I did the same myself, I have to admit, when we moved countries with a young baby. But this was partly due to the fact that my partner's life did not change in the radical way mine did after the arrival of the baby - he continued being a workaholic and did not give me much support. We are still living the legacy of this six years on. He has changed a bit now, after much pressure from me, and now is more of a participating parent, but I hold a lot of resentment, and somehow feel I have 'given' more than he has to the relationship/family set-up/country setting than he has, if that makes sense. Anyway, that is me, not you! My partner refused to go to counselling with me, so take heart that yours will. Make the most of the opportunity to try and find a way back to loving and supporting each other. Try not to panic about it.
But I really recommend you have some kind of therapy on your own to work out who you are and who you want to be. And you would perhaps do better to try this out where you are rather than making the dramatic move to the UK for therapy services. Have also started seeing a therapist myself (so thankful to find a British therapist out here!) and he is actually better-placed than someone in the UK as he seems to understand the cultural differences involved in mixed-couple relationships. This is definitely an issue for my partner and myself, maybe it also is for you? Cross-cultural relationships can be very enriching but also challenging.
It sounds like your shift to SAHM has not been totally satisfying, and you are not engaging with your surroundings in the way you want to (I understand so well your description of finding so much at fault in your new country! But it is the internal problems projecting, methinks). You might need to get a new perspective on your decisions and behaviour. You clearly need to find some more positive thoughts and influences to help you look forward. Therapy, as well as trying to make more community connections, might help you. Sorry if that sounds too simplistic, but it is well meant. Let me know how you get on.