We did the same thing when starting up our website. Actually, I felt it was a vital tool and suggested it and after several software glitches (or better yet my learning curve) it has finally taken off again.
If you strongly believe in the site and it isn't a negative impact on the family budget offer to pay any hosting fees (depending on who you go with) for the first 6 months (or whatever time frame you wish) until the site takes off and shows it's value to the PTO. Part of any reluctance may be that most see it is a technical black hole and scares them depending on how computer savvy they are.
As to the school having any type of input. We used to have a "page" on the school's website, which was fine but basically only listed the board officers. After we started our own site we were able to add so much more. (Our site has more pages then the school site currently does.) We link back to the school and they link to us so parents can go to either source and find out what they need and normally if one doesn't have it the other one will. We ask for input from the school but for the most part, since the site is maintained by the PTO privately, there are seldom any questions or concerns about anything posted. The largest advantage (and a great selling point to the school) is we purchased our own domain name. Yes, it cost more but the schools' site is linked to the counties main site so the web address is long and complicated to remember. The PTO's address though is short and simple and since parents know they can get to the school's site through the PTO site we are gtd. to have hits. Even if the parent comes with the intention of only going to the school site the chance of them spotting something and looking further on the PTO site is increased and makes it better for us!
We also do some of our ongoing continues sell items on the site and next year we are considering adding a forum board set up as well as start group email notifications from the site!
Take a look...
TES PTO Home Page
. I'm the webmaster (bottom of the first page) so feel free to contact me with any questions.