I've been thinking more about this and I think one of the reasons why BM's and stepmothers are at loggerheads, is because of the lack of choice in the relationship - very similar to that of a MIL and DIL, where neither woman would have chosen the circumstances in which they are forced to have this connection.
Except that it is even worse, because at least if you loathe your MIL, you can have some control over how she influences / treats your child. With a step-mother, you have no control at all. And as I said in my first post, with any other child-carer or person who has some kind of influence on your child, you have some control - teachers, childminders, nursery workers etc. are all educated or at least trained and vetted. With the "unsuitable" mothers of your kid's friends, you can limit the playdates or recognise the fact that they don't have much influence anyway; but with a step-mother, you have no control whatsoever. Now if you're lucky, your xp will choose to be with someone who has broadly the same values as you and although she may be different in detail (which can be irritating but bearable), in essence she's someone you would be perfectly happy to leave in charge of your child if she were a childminder, a teacher, a friend, or some other neutral carer and you hadn't encountered her in the step-mother role. If you're unlucky of course, he chooses someone who you believe is not suitable to look after anybody's children, let alone yours and in any other situation, the state would protect you from being forced to hand over your child into the care of someone you believe to be an unsuitable person. In this case, it insists you do.
The problem of being a lone mother with an ex who has a partner, is that you just have to accept the fact that this is what you have to do and you have to learn to do it with some kind of grace. (The Alcoholics Anonymous prayer springs to mind: Grant me the courage to change the things I can, the serenity to accept the things I can't and the wisdom to know the difference.) It's very easy for me to say that, because at present I don't have that problem; but if you don't come to terms with it, it has the potential to eat you up for years and ensure that the relationship between you and your ex continues to be a different battleground than the one you had when you were with him. And as long as the relationship is a battleground rather than at worst a neutral no-mans-land, that is very detrimental both to yourself and to your child.
And the other thing you have to learn to do, is continue to be confident in your own methods and ways of doing things and set firm boundaries and expectations for your child, so that even if she regularly enters another household where your values are not being upheld, you can somehow ensure that the values your child grows up with are yours, not those of someone whose values directly conflict with yours. And of course, recognise that as she gets older, your DD is going to increasingly be inluenced by values which are contrary to yours - but if you've managed to instill yours from an early age, then all you can do is hope some of what you've tried to teach, will stick.
It's very very tough to do this - it's tough enough to fight for your values to come through amid the constant and normal peer pressure and media and other noise fighting for our children's attention. And I think the constant undermining of lone parent's parenting must contribute to the poorer outcomes for children of lone parents; but if you're aware of it, then you can avoid falling into some of the traps which lone parents often do. The most common one being, not being able to distinguish between what is a genuine concern, and what is simply a kneejerk response to being forced into a relationship you don't want and wouldn't have chosen. As I said, very much like so many of us have with our MILs.
Sorry to go on, but I'm sort of half thinking aloud and hoping some of this waffle will be useful to you. 