DVD RW disks are well known for incompatibilities between different machines. The tolerances are extremely fine and there are several different proprietory formats in use. The disks work fine on the machine they are written on, otherwise all bets are off.
A cheap USB stick is a far better alternative for large file transfers.
217.910 kb file size is only a quarter of a megabyte and seems a reasonable size for a 310 page .pdf text file. Most email programs will easily accept this as an attachment. If the file size is in fact 217 Mb then the USB stick or a memory card is the most reasonable option.
CD/DVD drives are rarely used in commercial offices, so they tend to get gummed up through lack of use. Also the software for these devices is rarely enabled or updated for security purposes.
I fear the onus is on you to provide the documents in a format that the other party can use, so use a standard FAT 16 formatted USB stick with the files in either Microsoft Word or .pdf format, possibly both. Do not use any other file compression software.
Should the solicitor need to produce hard copies of the files, you will be billed for the time and materials needed.