The most common cause of regression in potty trained kids is stress.
Stress such as going to school, moving, new baby in the family etc are all stress triggers that can cause potty training regression.
The child may also notice that with a new baby that they are getting more attention than them so they decide to regress and stop going potty in the toilet like they normally would and want to wear diapers again.
Eventually the potty training regression will stop and the child will go back to using the toilet.
If you're about to move to a new house then it may be best to wait until after the move to do the potty training.
Keep the child in diapers until after the move and then potty train them a few months after the move is complete.
Allow the child to get used to the new location and new house before potty training.
Because if you potty train right away in a new house it may take longer for the child to potty train and they may have more accidents because they are not used to being in that house.
Although some kids are potty trained by 3 years old there's nothing wrong with a 3 year old not being potty trained and still wearing diapers.
Some kids may not be ready to potty train until 4 years old and I would not be concerned with the potty training unless the child is above 4 years old and getting near 5 years old and still not interested in the potty.
No 3 years old is not too old for wearing diapers whether full time or just in the night time.
Actually there really is no age that is too old to wear diapers as long as the child or person needs to wear diapers then they should wear diapers when needed.
Diapers are made for all ages and as long as you potty train the child they can wear diapers as long as they need too.
Some 3 year old children are potty trained and out of diapers in the day and some children are not ready to potty train until age 4 years old.
The child should eventually begin potty training on their own and decide not to wear diapers anymore.
However some children may not do that and may have to be forced to potty train if the child is 4 and not wanting to potty train.
Some kids are potty trained as early as 18 months old and some do not potty train until 3 or 4 years old.