There are a few different issues here :
I drive down a street everyday to get home. I use this specific street because there’s a four way stop and it really helps me avoid traffic accidents down it and I just feel safer using it.
This actually suggests you have issues of confidence and/or anxiety driving.
You should not need to avoid a four way stop.
I'd actually suggest you consider dealing with this issue. You're really creating other problems to try and avoid what should be a non-problem.
Today some a mom waves me over and accused me of speeding through their street everyday and they are afraid their kids might get run over.
There's always one person who thinks they own the world and that what they think should be the way things are makes them right.
Ignore this sort of person. Plain and simple. No good will come from trying to talk to them - they really don't care what you think or can prove.
The other times I’ve come down the street if there are kids, I always stop to make sure they are out of the street before I go. (Personally I wish they didn’t let their kids play on the streets but I’m not a parent and don’t know their POV)
Again, you're avoiding the "normal" route for one set of fears and seem to have replaced those fears with another set.
Is this route really doing you any good ?
I always go 20 mph, there is always a police man metering the speed because around here. If I was speeding, he would catch me.
So your speed is a non-issue.
I don’t really know if they just want me to stop coming down this street
Some people feel entitled to this.
Personally I grew up on a street off the main road, but we played football and stuff and when the cars came you just got out of the way. I can't ever recall any parents every rushing out to complain to drivers. To us, yes, we got complained to by our parents for not being more careful.
They simply do not own the street and you are entitled to use it.
I suspect they'd like to discourage it being used as a short cut by lots of drivers, but that problem is one for politics. Berating individual motorists is just road rage.
(again, I mostly use it because I feel safer at the 4 way stop it leads to) but I have a feeling they are going to try and get their kids to purposely block the road or something if I continue coming down the street.
All of this is about your anxiety, IMO.
And of all of it the only one you can actually control is choosing to drive down that street or not.
Is there a way I can talk to them so I can continue going down this street or I probably have to find a different path for now on?
Talking to some of the parents might work out but you are most likely to find one or two who feel entitled to what they want and who will not listen, and will probably simply get angrier. That's my experience with similar situations.
All you can control is what choices you make. I really think you're avoiding some aspect of driving you are uncomfortable with but need to get to grips with, and your avoidance is causing you this other problem.
I strongly suggest learning to use the normal route.
If you shift to a different alternate route you'll likely find the same or another issue waiting.
Driving is about making choices and avoiding one problem is only a good choice if it doesn't cause you other problems.
I'd personally prefer to run the risk of a minor hold up or small bumper-to-bumper tap than to chance driving down minor roads with kids on them. Kids are erratic, they don't understand risks, they are harder to fix than a panel on the car or a dent. So I think you're picking the wrong risk to minimize here.
EIT : From a comment of the OP's :
No dividing lanes. So no shoulders and sidewalks.
This, IMO, makes the choice of this route exceptionally poor. And it explains the anger of the parent(s), albeit misdirected.
Under these conditions it is not a road I'd recommend driving down because, from a child's point of view, there is no dividing line between "safe" and "not safe" on this road.
A comment on my original answer asks if I've misunderstood the reason for avoiding the original route. I'd again suggest that the OP is replacing one problem (whether it's time or personal anxiety) with a bigger one (increased risk of car hitting a kid). I think this boils down to a poor driving choice, at least from what I've heard so far.