I want to defend the shetland breed a bit here.
I'll declare my bias first though - I breed them, and have way, way into double figures. Not all bred by me, though some are.
They are an amazing breed, but must be handled like they're 16hh, not as pets or dogs. Give them an inch, and they'll seize it in their teeth, and gallop a mile. They are clever (some exceptions - I have one who is as dumb as a rock), loyal, brave, bold.
The one bit I'll agree with others on is that they do have a short stride, which can be a challenge if a child wants to learn rising trot. But if you keep them in a really slow trot, it's easier. My DC learnt and did all Pony Club on a shetland first time round. Are they a strong breed? Yes, if they choose to use it against you. But that's the same for any horse/pony. The key is finding one that won't. They can be limited to ride for the childs age, depending on your childs size - my DC rode their shetland until they were about 10/11.
Shetlands are out there which are amazingly perfect for small/vulnerable children. Depends what things you're prepared to compromise on. I helped someone find a shetland a few years ago, saw it advertised on Preloved, registered, in late teens (now in 20s and going strong), but it did have sweet itch. But they paid only £300 for it, and it's been just perfect. The children can do everything with it - it's a saint in pony form. It's LR/FR. It's not a speed demon - it's a VERY slow pony, but that's been perfect for their littlies to learn on and do Mini PC with. So much so that at PC rallies, the instructors keep asking if they can swop some of the kids off their whizzy expensive ponies, to borrow shetland saint for the other kids to do certain exercises on.
Given I have so many shetlands, including colts/stallions, I can assure you that if your fence is sufficient, they don't escape. We have no escapes. And I do have some who have escaped in previous yards with previous owners, but our fencing holds them.
They absolutely do NOT tow me or use their strength against me, with the exception of my working competing pony, who is not a childs pony, but an adults and fed to compete, and my stallion when covering inhand (not rude, but gets a bit keen, but we're still able to cover in a headcollar). But all of mine have been taught to be polite, I don't stand for bad manners.
They do NOT deserve the sh*tland tag they get given. When we have visitors to see the herds/foals, everyone agrees they're not what they were expecting, nor what people have told them they are. And any pony that comes in a bit highly charged, soon chills out here, and becomes easy to do within weeks. And I have very many, and have had/handled/bred/trained many more, so I'm inclined to think the issue there is not the ponies!
Is a shetland right for you? I don't know. Depends how much you want to do/your child is capable of. There are some saintly ponies out there, and not all for high prices. Of course, if you want a push button capable of some serious showing, you're going to have to look at paying well into four figures. But for a loving, safe pony, with maybe one or two compromises, they are out there.