Assalamu alaykum ukhti,
I'm sorry to hear about the troubles that you've been through, but trust me, there is light at the end of the tunnel, insha'Allah. From my own experience, converts to Islam are very highly sought after, and there are two reasons for this (and I'm speaking from the background of being from Middle-Eastern origin).
The first is that, generally speaking, they hold on to the deen more than those who were born into Islam and are apathetic toward it. There appears to be a growing movement among the youth (well, in my area especially, I can't speak for everyone) that whereas the parents used to be attached to cultural values, the children are now rejecting these in favour of authentic Islam.
I think being raised in this country has a lot to do with it, as we're generally more educated than our parents were, and we also mix with Muslims from different nationalities, so we have to put our cultural values aside and adopt Islamic values in order to get along (and it's far easier that way too).
As such, these people (and I include myself among them) seek spouses that have also thought about their deen, and made changes in their life to accomodate it (rather than simply following cultural practise which appears to be Islamic, but actually isn't when you look at it properly). And what better way to guarantee a sister has thought about the deen than to marry a convert?
The other thing is (and I mean this without being racist in any way, unfortunately this is just a fact of life), many men prefer white girls over darker girls. Especially among the Pakistani community, one request that is often made when a family is seeking a girl is that she be of light colour. So again, for this reason, white converts are highly sought after.
But there are negatives as well. The problem is the parents in most cases (most, not all). They're still stuck on their cultural ways, and they want a daughter-in-law that understands and respects it (from the point of view that they've grown up with it, so they understand it implicitely without needing to be taught it). Converts cannot offer this.
The other thing is, a marriage is not just about the groom and wife. It's a union between families, and families within a particular community tend only to know those families of the same community (i.e. pakistanis will generally only know other pakistani families). Thus, they tend to marry within these circles because they can do background checks on each other and decide whether they can be compatible with each other.
Unfortunately, reverts come on their own, which makes it hard to do any kind of a background check to establish what sort of upbringing they've had, or what the family traits are. These things are important.
And sometimes, you also get the potential husband who's a problem. He gets stars in his eyes at the thought of marrying a convert, but expects her to act like a native from his own country. I was once in contact with a convert from western europe who mentioned that guys would ask her if she cooked spicy food, but she couldn't stand spices to the point it made her eyes water. Whilst she didn't mind learning for the sake of pleasing her husband, it was something she physically couldn't do, and she didn't enjoy eating it herself.
All that said though, if you do find a guy open-minded enough, you may be successful, insha'Allah. It'll be up to him to convince his family if they need convincing, but you'll need to make sure he's marrying you for the right reasons (i.e. not to have you as a trophy wife).
With regards to your daughter, Allah knows best. There are several reasons I could give as to why this causes issues. A lot of guys like the idea of marrying someone who hasn't been touched, and the fact that you already have a daughter is a constant symbol that isn't the case. This also causes problems with the parents because of gossip (people like to speak ill whenever they get the chance, and for a guy to marry a girl who has children from another man, this is the perfect way to start malicious gossip and many parents aren't strong enough to deal with it, so they avoid the problem altogether).
There are also some (especially those who don't have their own children) who feel that they may not be able to offer your daughter her rights, and the fear in this case would be to do an injustice to your daughter in some way. There's also also the added fear that your child may also divert your attention from your husband, causing jealousy.
That said, if a man already has a child (i.e. is divorced), he shouldn't have any issue accepting yours. It's been my general observation that marriages usually occur between childless couples, or where both have children. But it's not unheard of for people without children to marry people with children, although usually it's where the guy has children (or at least custody of them).
Anyway, I hope that helps in some small way. Trust me, the right guy will come along soon insha'Allah. My only advice to you would be to go to where the type of guy you want/need exists. As my sheikh says "If you want a mango, you don't go to the orange market". You need someone strong in their deen, and also a modern thinker. Try going to the masjid, and also local Islamic charities, and join in with the public events that they do. You'll generally find (and I speak only from personal experience from my local area) that the people involved in these things are more forward thinking and perhaps more suitable for you insha'Allah.