No problems with DGD, but DD from birth, almost, didn't bother with tantrums, she was just determined at all times and in all circumstances to have her own way. She was un distractable, and if thwarted, would seem to comply but come back later and have another go. If we didn't do as she wanted she would 'punish' us by, in one case, running out in the road because she knew she shouldn't do it.
The only way to deal with it was to say no or yes firmly and stick to it. If necessary pick the child up or take her by the hand and make her go where she should be. We didn't have a naughty step, but she would be sent up to her bedroom for specified periods of time.
To limit conflict we tried not to have any rules for her behaviour that were not essential for security or the proper conduct of life - not being rude to people, or disrupting the lives of others. Unless other people were involved we did not ask for apologies. Compliance with requests was taken as sufficient. It wasn't easy, but we won through and she is a caring and loving adult, although still with that very strong will and uncompromising personality, which she recognises.