I'm SO pleased you live somewhere beautiful and are going out for a walk to enjoy it, please remember how lucky you are to be able to do this, and enjoy it for me too, as I'm currently stuck in bed again.
I'm also pleased to hear that you're planning on getting a medication review, I really hope that they give you something that will help you feel more like your normal self, which is bound to help you cope.
With regard to the fact that you say you seem to be getting on OK, and then he comes back into your life demanding contact, is there an access arrangement in place, or is it just a case of him turning up and demanding to see the children? If it's the latter, tell him to get lost, and DO NOT LISTEN to anything else that he has to say, just put the phone down, or shut the door in his face. If he wants access, then let him get it through the courts, which I doubt very much that he'll bother to do if he lives abroad.
Maybe it's time to start thinking about dating again too. I know that's probably the last thing that you want to do, but wouldn't it be nice to give some other lucky guy the chance to tell you how fabulous you are, instead of allowing this gerk to pull you down every time he pops back into your life?
I can totally understand the feelings of loneliness at this time of year when you only have little ones for company, but try reframing it, and thinking 'I must make the most of this time with my kids, as they'll have grown up before I know it'. Most of us don't appreciate how quickly they will grow up, until it's happened, so I really do encourage you to enjoy it now, while you can.
Also, do you have any hobbies that you can do during the times when you're alone, or do you tend to just sit and watch TV or scroll the internet? If it's the latter, then maybe try something new, that's where the internet really comes into it's own, as not only can it give you hundreds of ideas of things to try, but you can also usually find free classes online to learn them.
Finally, I'd like to take this opportunity to wish you a VERY Happy New Year, OP, let this be the year that you take back your power, and shove the arsehole that left you, so far into the past that he's but a faint shadow.