It's very difficult to separate the issues of maintenance and contact. Some men feel that, if they don't have contact, it's OK for them to stop paying maintenance. It's not. Equally, where an absent father pays little or no money, some women feel that they shouldn't have contact. Again, that's not right.
Even if he can't put the needs of the children first, you must. They need to see their father and will thank you for facilitating this when they are old enough to appreciate it.
All you can do is point out that his getting at you by withholding maintenance (or at least a decent rate) is eventually going to backfire when the children realise what he is doing.
If you're not happy with Reeves & Co, try Sharon Hawkins at Berry & Berry. They do legal aid. If Sharon isn't available, she has at least 2 colleagues who specialise in family law and will take on legal aid clients.