You should get advice from an attorney in Utah because holographic wills, if allowed in your state, are subject to specific statutory requirements. In Idaho, holographic wills are allowed and must be entirely in the testator's handwriting, indicate testamentary intent, be dated and signed by the testator.
In addition, the probate code in your state most likely includes provisions relating to how one must disinherit heirs. If children are not mentioned specifically in the will but omitted, they may make a claim against the estate arguing that they were omitted by mistake. Therefore, it appears that the language your husband included in the will may meet this requirement, however I am not licensed in Utah and cannot give you legal advice about the will your husband wrote. Again, to be safe I strongly suggest you obtain legal advice in Utah from a qualified estate planning attorney. I would suggest you go to www.nelf.org for a list of attorneys in your area.
Holographic wills can be acceptable and enforceable in Utah. They can also be challenged in court, and the children your husband is trying to disinherit may be motivated to try. There are numerous grounds upon which a will (including a holographic will) can be challenged and deemed unenforceable. The only way to minimize that risk is to utilize an attorney.