I have 20 years experience of keeping Green Iguanas. I kept 5 in that time, all until they died of old age/illness/natural causes and had a fair few rescues in and out during that time too. So, I have a fair bit of experience with them.
Yes, they are specialist animals with specialised housing and dietry requirements. An awful lot are kept incorrectly and the results for the animal if this is the case can be fatal, but when kept properly they are very rewarding animals to keep, although I would never class any reptile as a 'pet'.
Green Igaunas can be extremely aggressive when adult and are not for the faint hearted. A lot end up in rescue for this reason and due to their adult size and for the same reasons responsible reptile shops will not sell them any longer. That said, I have dealt with some very aggressive animals and never been hurt badly.
Adults need a room sized enclosure, which must have an adequate ambient room temperature and several hotspots, plus ideally a pool large enough for them to fully submerge in and climbing/basking areas.
ALL reptiles can carry salmonella, so good hygene must be practiced when handling them or dealing with their enclosures. There's no reason this should be a risk to children if good practices are followed. I personally would keep an aggressive adult iguana in the house with children, but I wouldn't have it out around children if it was aggressive beyond what was normal as a precaution.
I would never, ever, in a million years allow an adult iguana free access to a garden. They can be very quick and it would be fairly easy for one to escape. They can get their UV requirements from artificial sources and a garden is unlikely to be warm enough even in summer for an iguana. I also wouldn't have one free roaming in my house. These are wild animals that are not domesticated and IMO it would cause undue stress to the animal. They tolerate handling, but they never like it. They are not pets.