Do some research -- pull up newspaper articles online about how landlords are held legally liable if someone is injured on their property, even if the injured person didn't have permission to be there. Find state laws on liability. Take this information to the landlord ASAP and also take anything you have like photos of these kids on the property. Then tell the landlord very clearly, "These kids are becoming a nuisance and I now realize that if one of them gets hurt while on the property, YOU could be sued as the owner, even if you are not living there yourself, and even if the kids shouldn't have been there. Our quality of life in your rental property is now being affected daily and negatively. So we are requesting that you put up a fence as soon as possible, or you may end up being sued and we may have to find another place to live. Because we are next to an apartment complex, there are always going to be families who think this property is common land. We need a fence and you MAY be protecting yourself legally by getting one."
I suspect that this family may actually just have the mistaken idea that the property IS communal, or belongs to the apartment complex, or they may be assuming if it's not fenced off it's fair game. Have you ever just asked, "Hey, we know the kids like to play there, but we're not sure if you realize that this is privately owned property -- not common land, city land, or the apartment building's land. Our landlord owns it." Have you asked that just to see how the parents react? Just asking the question could end the whole problem!
Start with that, then you need to be assertive since you were not assertive early enough. If they act like they had no idea they were on private property, follow up and tell them, "Our landlord is now concerned about liability so he's asking that the kids not play there any more." If they get all huffy and angry about it, you need to stay cool and just repeat, "We and the landlord are asking that the kids do not play on this side of the bushes any more, because it's not common land or apartment property, and the landlord is concerned about wear and tear and injuries."
If the landlord won't put up a fence, well,, when you see the kids there again you will have to speak to the parents EVERY time or start having the landlord phone them -- is the landlord up for that, or is he a hands-off landlord who's going to do nothing and leave this all on you? If so -- I really would consider finding a new place to live because a useless landlord plus intrusive kids plus neighbors you have to face every single time you walk out the door equals a complete pain to me. You don't have to sell a house to get out of this, either.
I hope your husband was joking about the swing set - right? Put that up without a fence and you will have the next door kids and every other kid in the complex using your yard like a park. I would not invest in something like that anyway if I were renting, unless I planned to stay a very long time, and if these apartments are looming over you like you describe, I'd really be thinking of finding another location unless something vital like school district is involved.