I am looking for some objective advice about my ExH, I posted here last year about the crazy situation and you were all very helpful. Here's the thread for the backstory - www.mumsnet.com/Talk/relationships/a1951305-My-husband-has-left-me-and-doesnt-want-to-see-the-children-anymore
So my EXH hasn't seen the children in about 10 months. Last Friday, my ExMIL was visiting and handed me a letter and told me my ex had written it to me. I didn't want to read it but thought it may relate to DC. I opened the envelope & found 4 pages of him rambling about how what happened was a 'moment of madness' , that he is still in love with me and thinks about me all the time. He said he understood that he did damage to our DC and wants to make it up to all of us. He wrote that he wanted to see the children again that he misses them and that he had a wonderful relationship with them before he left, which is true. He also wrote down his new address & phone number and told me to call him if I wanted to meet up and he would go 'anywhere in the world you want to go' 
However, our children haven't even mentioned him since new years eve. Our DD is 6 and our DS is now 8. Whey both have settled lives, great friends, and love their new school. Te moved away since my last post as I felt we needed a fresh start - and they are really great children and I don't want to ruin that. Im still wary that the abandonment will have some sort of impact on them in the future and I can't guarantee that he won't walk out of their lives again, creating even more upset. He probably will since he already did it once.
On the other hand, I don't feel I have the authority to stop him seeing the children, and of course I would prefer them to have contact with their father but I tried so many times to get him to maintain the relationship with DC, even offering to drive them to ExMIL so he could spend time with them without even having to see me, each time he said no I don't want to see them and I gave up in January. My ExMIL says he often asks about us, and always wants her to ask if I am seeing anybody. She respects my privacy and doesn't ask me questions like that thankfully. I did start dating my boyfriend in March, but I haven't told anybody about it and he hasn't met DC as we are taking it slowly. He knows all about my ex and was disgusted when I told him, he is such a sweet guy. But honestly, when I got the letter from my ex it sort of threw me off, I don't want to get back with him and I never would, but he was my first and only serious relationship, we were together 13 years and married for 10 and our relationship, apart from the obvious was perfect. I doubt that I will ever love anybody the same way again and I think part of me still does. He also gave me our beautiful DC. I was surprised at how affected I was by the letter. After a period of anger and hate I achieved some indifference towards him which has now been ruined.
Then on Saturday I got a call from my MIL's house, when I answered it was my ExH, which again threw me off because I haven't heard his voice in months. He asked me how I was and could he see me & the children. I told him I needed time to think about it. He cried on the phone telling me the past few months have been horrible and that he just wants to see me again, and then he offered to take the children to school on Monday or meet them with my exPIL - I said 'no this was your choice' & hung up.
What are my options here? We officially divorced 6 months ago - I obviously got full custody and I have signed documentation, emails and texts that clearly show he wanted nothing to do with our DC. But when they get older I don't want them to blame me from keeping him from them, it's a really difficult situation and I have no idea what to do. Im sorry this is rambling a bit but I thought this was all in the past and the letter and phone call & re reading my OP bought me right back to that place I was in 10 months ago. Im not sure how I would feel if I saw him again.