"Night-time" dryness.... is not even attained until a child is about 7 years old, + or -
And this is NORMAL.
MANY Kindergarten kids still wear night time diapers.
Normal.
For naps or night time/bedtime, just use a waterproof bed-pad under them. That is what I do... and it makes clean up much easier, and I have about 4 of them that I just switch out as needed or if my kids leak or have an accident. No biggie.
This is normal, and biological. Full night-time dryness and control... is different than day time potty ability. These are 2 very different things.
They are very young.. to be expected to be dry at night and/or for naps. And you CANNOT control their bladder.
If you expect them to be dry at night, and restrict liquids etc., it will just make you AND them frustrated because it is not an appropriate expectation. Your kids are normal.
My daughter, was 5'ish, when she was able to be dry at night.... until then she was still wearing night time diapers.
My son, is 3.5 years old. He wears a diaper at night. He is pottying but he is not a full fledged rocket scientist about it yet. NO biggie.
A child, will not potty "train" until they are ready. My son even told me "IT'S MY BODY!" and that's it.
Your kids are NOT ready for underwear at night... nor are they ready for being totally potty able... nor are they ready for the expectation of being potty able yet.
Pull-ups in my opinion, is useless. They leak, they don't hold much. And it is useless for night-time use... because they don't hold much. So you WILL inevitably have leaks. Not the child's fault.
Just use night-time Diapers.... Huggies makes them.
If your child won't poop in a toilet... let him poop in the diaper. That is better than them getting constipated... or developing Encopresis. And boys.... are typically later in potty ability/attainment/training.
If you get 'mad' about their inability, it won't help. They can't help it. Prizes/rewards never worked with my kids and I don't use it. The kid... has to be ready for pottying... bottom-line.
All the best,
Susan