To break the deadlock you simply have a vote.
Which ever opinion receives the majority is what has to happen. Doesn't mean it will be the correct course of action according to tax law but it seems to me that PCs can pretty much do what ever they like so long as it is a majority vote - there simply isn't the mechanism or will to challenge.
After a vote it becomes a corporate decision which could be questioned by internal / external audit (but is highly unlikely to be and even if it is would make no difference what so ever.)
Your biggest problem is HMRC, they will want their VAT and will care little about who pays it. Those that are seeking to prevent the PC from paying the VAT on the grant will probably end up with the PC paying the VAT on the grant anyway if, as you seem to indicate, the VH has no sustainable bank balance of its own.
If the PC is the sole managing trust and the village hall gets all of it income from grants + PC, what does it really matter if the PC pays the VAT - if the VH doesn't have any funds it can't pay the VAT but HMRC will not care so long as their get their pie.
On a tangent, the bigger problem (IMHO) is a VH which (as I interpret from your post) is not managed as a going concern that can wipe its own face.
It's all very well having initial build and significant upgrades from grant funding, but any entity must be able to pay its own way with receipts covering general running costs.
Do the PC trustees of the VH have a credible business plan or do they simply rely upon the precept to balance the books?