is, don't waste your time on him anymore. You've given him enough opportunities to respond, and he chooses to ignore you. How do you know for sure that he hasnt opened these letters?....if he is anything like my ex, he will stuff them in a drawer and ignore them, they appear to apply the no contact rule so much easier than we do. So what if he suddenly gets in touch, which I think is unlikely especially with the footie on the telly, and what they get up to now, is really not your problem. Most of what you imagine he is doing, is surely only your imagination, not actual fact.
Bless the fact that you are able and capable of organising the children with childcare, that you have a job to do, and that you no longer have to second guess there actions.
As for the solicitor, just use them to deal with legal things not emotional.
He is still pulling your strings whilst you let him even though he hasn't even been in touch with you, you are still waiting with baited breath for his responses.
Carry on as you are, you really are a strong, capable lady, who absolutely doesn't need his approval, opinions or intervention.
The children will be fine, just as long as you are around to give them all the love and reassurances that they need, and a hug and a kiss too.
Hope you enjoy your weekend.
Ka3n