There are a few points here, please don't offer advice on the past, I know we've made mistakes with this but cannot change them now. Although I've been a cat owner before and this time it was mostly fine with one DC, it's really gone to pot with the second DC.
Young cat has been stressed on and off since just before my pregnancy - would not come in when there were visitors, which meant my husband would have to pick him up and take him up to a spare room he stays in at night which is his own space. Although not many people come by so it wasn't often. Then, when my baby was born and would cry, he would hunt around for him and sit by him and cry with him. The baby doesn't cry an awful lot anymore so it's not caused by that as much.
Although they have always been as thick as thieves, my 5 year old has recently picked up a habit from school of high pitched screaming when she doesn't get her way which would stress the cat out. She's had a stern talking to but forgets herself at times.
Two days ago, the cat was moping and crying (I think it was triggered by her screaming the night before but the crying was actually in chorus with DC2 crying), I had a conversation with my 5 year old about whether our cat could cope with loud noises, children and visitors and whether it might be fair to give him to someone older who has a quieter home because he doesn't seem well with a busy house. I feel awful about this part but I said it to try to rationalise why we might need to look to re-home him out of fairness to his wellbeing and because I wanted her to be on board since he's her pet.
Yesterday, I managed to get the cat to eat a dose of a stress relief tablet prescribed by the vet, after being unable to get him to take it on Wednesday. He seemed better, I gave him space but he had fusses from DC1 and DH during the evening. DH let him out this morning and didn't give him today's dose first thing with wet food. I've called the cat on and off all day but he's not come home. No sign of him anywhere in our garden.
We will speak to the immediate neighbours but how do I explain this to my 5 year old?