So you are willing to let MIL's behavior, 10 years ago AND now, dictate your life choices? That's what you're doing here by rejecting these cousins without so much as talking to them about this. Yes, it was less than courageous for all those cousins to dump you after her lies way back when, but it IS courageous of this one family to try to rekindle your relationship now. Why punish them for making an effort? For all you know they may have some deeper reason to want to see you and know you again. The last time someone from my long-ago past got in touch out of the blue (though we had not fallen out as you and these folks have), it was because she had found out she had terminal cancer and she wanted to touch base with her past. These cousins may not be dying but they may have reasons to want to step up, apologize and see you again. Maybe they just MISS your family and now are mature enough to realize they should never have let MIL get between you.
People do change. They seem to be trying. Why can't you try too?
I would not agree to keeping things secret. But neither do you have to broadcast to MIL that you're seeing them. It sounds like MIL lives close enough that she's going to figure it out anyway. But I would tell them you are done tiptoeing around MIL's obvious illness. Still -- no need to announce to MIL that you and they are seeing each other. If she finds out and blows up, your husband (not you, him!) should deal with her but not by rejecting these overtures from the cousins. If he does that he's letting her illness run his life for him.
It sounds as if you and your family live geographically close to MIL, if people from her church walk up to you and if you're spending five days at a time with her....Distance would be great, but if you don't literally have distance, why are you not putting some distance between you by NOT being with her "Saturday and Thursday and they spent five nights at our house before that"? Why is that much togetherness happening with someone who lies and lies about you? Why? This is on your husband and you for letting that level of contact continue. It's way past time to be too busy with your own lives to spend that much time with a relative who destroyed your relationships with FOUR other families and who spreads lies as easily as she draws a breath. Maybe your husband is being a dutiful son and sees her as sick (which she is), but I dont' see why he tolerates his mother being in your family's life that often. See her, yes, but control the amount of time.
You have kids. Kids have activities. Time to be too busy to see her this much. Husband can go see her on his own if he feels he must and you can limit your exposure to her to just seeing her at group events where other people are around.
I wouldn't host or be hosted by someone who lies about me all over town, even if she is a relative. We have one relative who is unpredictable due to mental illness (like your MIL, except she's very paranoid and diagnosed as such, but wont' get treatment). She can be just lovely and sweet, or she can be in one of her periods when various relatives including us are "the enemy" and "out to get her." But we know better than to ever go to her home or have her to ours -- we meet on neutral territory for limited periods of time, just a lunch out and a walk around etc., with a definite meeting time and a definite departure time, since we never know if she'll be Nice Aunt or Accusing Aunt. Time for you to limit how and when you see MIL as well.