Whenever there are strides being made in workers' rights there are no doubt lobbyists of equal or greater influential caliber devising a way to vehemently undermine their progress simultaneously. Because management wishes this were a 3rd world country with no basic regulations over the workplace, they hire these goons to try and curry legislators' favor to try and justify lowering ourselves to that standard or horrid living (10-12 hour work days, zero protection from occupational hazards etc). So union laws do affect anti-labor lobbyists quite ironically, they feed the fire which burns them.
The universal truth in the United States is that if you have enough money, you can work around any laws you like. An example of this is Citizens United, in which donors are allowed to donate any amount of money to political "Super-PACs," which are technically not tied to a candidate. In this same vein, the anti-labor lobbyists simply change the rules or use obscure workarounds to ensure that their agenda continues to be pursued, in flagrant violation of the spirit of the law, if not the letter.
Although union laws are set up to protect unions and the people in them, there is a long rich tradition of anti-labor forces ignoring those laws when they see fit. There is simply too much on the line for anti-labor forces to roll over and capitulate on what they see as the most important issue of the day.
No, I do not think that union laws are in any way affecting union lobbyists as they try to push through an anti-union agenda. I think that union laws are designed to help those who are unionized, and only the unions of which try to carry out the rules and bylaws within them.