In theory, a contract awarded to a company connected with a councillor is not in itself forbidden, but the procedures by which that contract is awarded need to be totally open, transparent and with appropriate declarations of interest etc. made. I would expect all such potential contracts to be agreed by full council even if they fall below the threshold for comparative quotes per your financial regulations, for quotes to be anonymised and when payments are made to the contractor, those payments to be approved by full council even though they may fall within a delegated authority to authorise granted to a committee and/or officer. Whenever the work, specification for the contract or discussion on the contract or payments to that councillor comes up in a meeting, that councillor must declare an interest an leave the room. It doesn't sound like any of that is happening.
A council nearby to me is currently dealing with the fall out from something like this from some years ago. It is not pleasant and the police are involved with allegations of fraud.