FAB it's great to tell your children how much you love them and how much they mean to you, but not just after they've just being playing up and accusing you of bad parenting. I would leave it for when you catch them doing something like playing together nicely, or offering to help, or making you laugh, or in a neutral moment, like bedtime or first thing in the morning.You also show it day to day in your care of them, your concern for them and by spending time together, hugs and kisses.
They already know you love them, they are pushing your buttons with those accusations and are hitting the jackpot with your response. Remember you don't have to answer an accusation of 'you don't care', silence can be a good response. Later on,when they have cooled down, ask them if they really feel that or were they just cross because you weren't doing what they want you to do. They have to learn to deal with things not always going their way, it's part of growing up.
If you could convince yourself that you are a good parent, and you sound like one, it's like a flak jacket, the dcs will know that you are not going to be shaken by any accusations of being mean, it will just bounce off you. They will sense your confidence and not say things like that anymore. Mine don't.
If you teach them how to ask for what they want without whining and how to assert themselves when someone else is being unreasonable, you are doing a good job, and preparing them up for the future.