So sorry to hear about your dog. We lost our Oldgirl to bone cancer last year at just shy of 14 years old and it's a truly evil disease. 
My dcs were 11, 9 and 4 and we were open and honest from as soon as she was diagnosed. We explained that she was in a lot of pain, that the medicines we were giving her were helping to keep her comfortable, but she would reach a point where they wouldn't work anymore and she would be in constant, serious pain, so the vet would help her die, rather than letting her suffer like that. We explained that she would die soon anyway, but that she would experience a great deal of pain first, so it was kindest for us to make the decision not to letter her suffer and ask the vet to help her pass sooner. We also had to tell them that she might fracture her leg at any moment, so they had to be really careful around her. We all had a good cry and each of us had some quiet time with her over the next few days.
Our intention was to tell them before we took her to be pts, so they could all say a last goodby, but as it happens, when we took her in for an xray to check for lung mets they discovered that, not only was she riddled with mets, her leg had broken right through and we had no choice but to pts there and then. The dcs had known we were taking her in that day and were upset, obviously, but had already had chance to come to terms with the fact she would be gone soon and each had had some time to sit quietly, stroking her gently and talking to her, so I guess they'd already said their goodbyes really.
We took her ashes to her favourite beach during our Summer holiday and scattered them there, making a special trip in the evening so it was quiet and private. The only one who got upset at that was my youngest (dd aged 5) and that was because her eldest brother was rather insensitive with his language about what we were doing, but as he has ASD, it wasn't really his fault and once we'd had a good talk and given her chance to cry and let it out she was ok again.
A year down the line, we still miss her, the dcs still talk about her often, but we are able to look at photographs together and remember the good times fondly.
I wish you lots of strength through this difficult time. 