The first thing that I would say is that NO dog is 100% trustworthy around children.
Children don't understand dog cues - such as growling and signals to be left alone - which is why so many end up being bitten by the family pet (I'm thinking of my sister here many years ago, I was telling her not to blow in the dog's ear because he didn't like it, but she kept doing it - 6yo's are not the brightest, and three stitches later...). Your niece was given lots of clues no doubt, but ignored them and so was given the 'more serious' version of a warning. Be firm with the child, and provide the dog a place to escape from the tots. Crate training is likely to be a godsend in your family situation, please do it - it will also give your dog a place to hide from the kids when he's had enough fun and games.
So supervise all interactions and tell the children what the dog is doing to tell them they're being annoying. Education is important.
Next thing - by allowing the dog to be on you, you've given him a 'promotion' in the pecking order, so to speak. Without having been there, its hard to say, but there is a chance he thinks that he's higher that your 22 month old. This happens frequently, mostly because 22mo toddlers are not exactly together in the communication and mobility stakes. They are not 'in charge' of anything, so dogs can mistake that for being like a 'puppy', which is a reasonable (if incorrect) assumption. The dog might think he's 'alpha' to any puppy-thing.
What to do - dog on the floor at all times. Dogs do not sit on laps, nor are they invited for cuddles or to rest their body on you. Make sure your dog sees you carrying your toddler, and sees you rewarding the toddler BEFORE he gets anything. If you are on the floor, the dog can be beside you, but not on you (I say this, although my DH allows our youngest Elkhound to lounge all over him - but she doesn't do it to anyone else, its their 'thing').
Also teach the toddler to be in charge of handing our some sort of regular treat. My DD started giving our dogs their evening treat around that age, with my hands-on assistance (my big dog wouldn't take them from her otherwise).
Finally, he may be slightly 'possessive' of his things, including food and treats. This can be a problem if you don't address it, because there will come a time when he has something in his mouth that he cannot have, and you want him to hand it over without a fuss.
Usually, for toys and objects we use the 'give' command, and reward/swap a treat for the object. I'd suggest that you, and the kids play this training game. You should start until he gets the hang, then let the kids have a go at offer/swap, until he is happy to relinquish whatever it is he has in his mouth. Eventually, he'll work out that bringing things to you and dropping them might also be reward-worthy.