I was an active witness for over 40 years. When my husband started posting on this site and telling me things he was finding out I was shocked and concerned. But I told him to take research seriously to subject what he was finding to critical review and check his facts. I told him that it was dangerous to accept things on face value and give the organisation less credance than sources that could not be verified.
I am a strong believer that if something is true whatever is said will not turn truth to a lie. I was prepared for difficult revelations, what was important was whether these would be enough to change the way we chose to worship. It took a while for me to stop trying to block out what was being said and be prepared to debate the points he raised. I still have problems if I feel someone is being too facetious and dismissive or if he isn't listening to me.
You must remember that no crime is greater and nothing so much to be feared as apostates. Their powers are remarkable, they can mislead you and shake your faith. To her you are associating with extremely dangerous people. This clouds her reasoning.
The way I would approach it is to ask for a time when you can properly discuss the issue as it is important to both of you.
Explain to her why you feel the site is important to you and ask her to specify what she objects to.
Repeat back to her her objections and try to establish exactly what her concerns are. If it is the amount of time you spend on the board assure her that you will spend no longer than she spends on her theocratic activities.
If it is exposure to apostates remind her that you don't scrutinise her associates at the meeting. Nor do you restrict the topics she discusses even when they are derogatory to non witnesses. You will not force apostate teaching on her but she is free to ask you about what you have discussed on the board. Assure her that you will look into anything you are told and not take statements on face value as far as the organisation is concerned.
You respect her right to worship in her own way and as head of the house you would appreciate similar respect from her regarding your search for religious truth.
As far as your daughter is concerned assure her that you both have your daughter's best interests at heart. That when the time comes for her to choose her path in life she will assuredly be old enough to make her own decisions. Your wife can show her what her religon has to offer but she must also allow you to present the alternatives so that your daughter can make an informed choice.
Remind her that you love her dearly that this is not a test of who loves who the most. If she is insecure and jealous she may be concerned that you might meet a like minded single on this board. You need to remind her that she is special and important and if it wasn't so important to you you wouldn't have a problem complying with her wishes. Because your relationship is important to you, you are happy to make some compromises in your life even sharing her with her God and an organisation, you would hope she would have enough love and trust in you also.
After all if you cannot use the board where else would she suggest you go to let off steam occasionally. You could picket the hall or would she rather you joined a coven?