We have not had the "trouble" of teachers wanting to be on the board. We actually pay them! You are lucky in a lot of ways to have a rep from the school. I think changing the by-laws are very important.
In the past we did have a teacher as the secretary, but for only a year.

Our board currently consists of eight members, two of which are spouses of teachers. Unfortunately, these two individuals are constantly sprinkling us with "inside" information which only serves to highlight how under-paid and under-appreciated the school's teachers are. We are constantly trying to keep on track and not allow ourselves to be changed into a teacher's advocate group. This may not be the case in your situation but be careful. We knew that these two individuals were coming in with an agenda but our principal believed that talking to htem beforehand would be enough to keep them reined in. She was wrong and is learning that now.

I feel very strongly that we are a PFO (Parent Faculty Organization) and as such, we should encourage teacher representation and participation. At the same time though, and Tim mentioned this at the conference, teachers are expected to do more and more every year, so if they don't want to participate or don't have time, then we have to respect that. Our school is very lucky to have a lot of teachers on the Board and at meetings. The principal, ass't principal, and 3 teachers are on the Board (as VPs and corresponding sec.) and we usually have about 2-5 staff members at meetings. I think it's because the school community, including the administration and parents respect the opinions of teachers.

We allow a teacher to hold only v.p. or secretary per our by-laws. All teachers have voting rights. Good luck.

On the other side of the coin, our current presidents are teachers. One has a child in the school, one does not.
Teacher participation has been poorer this year than in other years. Don't know if there is cause and effect there. I have been underwhelmed by their performance as PTO presidents.
I would love to amend our by laws to exclude them as officers but agree that could turn contentious.

PS...my secretary is a fourth grade teacher and mom of two, my best advisor is a reading special teacher mom of 1 and a sixth grade teacher.

Best team I've had in years........