The fact that you proved one of the charges indisputably false should cast serious credibility issues on all other charges - at least the ones of the younger child.
I know someone who had been falsely accused of beating his ex-wife and was banned from seeing his daughter for years. He finally proved the accusation to be false when he got the date of the woman's hospitalization and police report. He had been in another state busy at work during that entire time period and had a rock solid alibi. Her accusation was indisputably false.
His lawyer argued that because the woman's primary accusation (the only one that involved hospitalization) was clearly a lie, all other accusations should be seen as lies. The judge was swayed enough to order supervised visitation, which the mother eventually caused enough grief (including violent actions of her own) to get stopped. Judges often "err on the side of safety" even when they highly doubt that there is any truth to the charges.
Your trouble isn't with the judge, though, but with CPS. This might also have a lot to do with the imperfections of your husband that you mentioned or even the issues with your Mother In Law. CPS agents may see lots of holes in the specific allegations, but still feel uncomfortable with your H as a father anyway. They may be using the allegations as an excuse to play custody judge.
I know a guy who was accused of child abuse by his ex and was under investigation. When two ladies from CPS came to his home, he was indignant at their lines of questioning. Instead of realizing that they were just doing their job, he was insulted at being under their microscope and he became belligerant. No, he never became violent, but the women left, saying that they felt unsafe with him. With no evidence whatsoever the man had his contact with his daughter cut off.
I don't know if your H has similar anger issues, but these CPS folks have your children's fate in their hands and any parent needs to be on their best behavior around them.
I don't know what is going on in your case, Elizabeth, and I won't ask you to elaborate on what you mean by "not perfect", but I will say that my heart goes out to you, your H and your stepchildren. If the children are lying, you can bet they are being heavily coached and manipulated. Don't blame them for this.