My two call me dad in the home (they are 12 and 14) and have done since my transition two and a half years ago. I'm not their mum, they already had, and have, one of those.
Prior to counselling I remember with a cringe saying if they call me dad in public I will just walk away. Of course it was pointed out to me that they are children, so what else are they going to call me? I imagined the world would stop spinning if it happened, but of course it doesn't.
My children know they can call me whatever they wish and I think they should have the right to do so as long as it is respectful. If the price of that is the odd embarrassing moment for me then for the sake of their wellbeing it is so totally worth it. Incidentally, without any prompting, they seem to be choosing to call me Mandy in front of their friends, and that is fine with me but dad would be ok too.
Transition is potentially hard on the children so we try to ease that burden by letting them determine what happens to them. Thankfully this has resulted in them being confident enough to ask me not to attend a parents' evening and to nag me to death to come to school concerts and shows they were in. In fact my daughter is a little cross that my GRS next month will prevent me from attending her next show and her guest slot fronting a band! I much prefer that situation to them suppressing their feelings and then possibly feeling awkward just to avoid potentially upsetting me.
Things are probably different with much younger children of course and I have no idea if that makes it easier or more difficult. I wouldn't suggest our way should work for everyone, but it works for us and it seems to have made life easier for our children than it might otherwise have been. In our role as parents that has to be the main objective doesn't it?