Gidders, this sounds very familiar. We have lots of babies like this on the 'Challenging 3 month olds' thread, so you might find it useful to have a read through some of our escapades.
I could only get my DS to sleep in a sling during the day between 9 weeks and 12 weeks (at night he would happily feed to sleep, but never, ever in the daytime!) He would wake lots at night and be virtually impossible to re-settle after feeding. On the other hand, I know lots of people with non-nappers who do sleep wonderfully at night, so it's not that unusual.
Since then I have had increasing success in getting him off without the sling (he's now 14 weeks). Partly that is him being older and easily to settle, and partly I've got better at identifying his tired signals. There's an explanation of my 'method' for getting him off on the 3 month olds thread in case that helps you.
DH and I spent most of our evenings for a month pacing the streets with a (crying) baby in a sling. Today for the first time we didn't need to use the sling at all in the evening.
I wouldn't worry too much about the late evenings. Babies have their own ideas about when day & night are, so IMO it's best to work with them rather than against them. Up until about 12/13 weeks old, DS could never be persuaded that it was bedtime before 8pm (then 9pm, once the clocks changed!) but in the last week or two that has been gradually changing, and today I managed to persuade him it was bedtime at 6.45pm! The most important thing IMO is that she is sleeping well at night and that you're getting enough sleep to cope.
I would ignore your MIL. My mother thought at first that I was neurotic about DS's sleeping, and (I suspect) thought I was 'doing something wrong' because DS was so difficult to get to sleep. After spending a bit more time with him, she was much more sympathetic to our difficulties!
Lots of babies who struggle to nap during the day will only sleep for about 30 mins at a time, so don't worry about that. A paediatrician friend who recently gave us some advice on DS's sleeping said that it's perfectly normal to only sleep for such a short time and we shouldn't worry about it. Some babies 'graduate' onto longer naps once they're a bit older.
One thing that makes a real difference is being able to identify your DC's sleep cues and try to get them to nap then, as you're much more likely to be successful. Signs include yawning, grizzling, a starey look (but these vary from baby to baby).
I found this page useful - it gives rough averages of awake time for babies of different ages. If you can't spot your DD's tired signs, try getting her off to sleep once she's been awake for the average length of time babies of her age can stay up. If she likes the sling, then probably motion in your arms is a good way to start. I tried jiggling DS upright, as if he were in the sling, but he didn't like it, whereas cradled in my arms and jiggled was much more successful. If she will take a dummy, that can make a real difference too, so keep going with that. I find that swaddling helps - it might suit her as it might feel cosier, like being a sling.
The No-Cry Sleep Solution by Elizabeth Pantley has some good suggestions about changing babies' sleeping habits without leaving them to cry. One suggestion is to get them to the point of very sleepy in the sling and then take them out and try settling them in the cot or in your arms. I've not tried it myself, since I have a baby carrier that would be hard to extract a sleepy child from, but it might be easier with a single ring sling. I think this would only work though if you've caught your DD at a time when she's naturally sleepy.
FWIW, everyone else in my NCT group seems to be able to put their baby down for naps too. I found it very isolating until one of my friends told me that her daughter spent her first 4 months in a sling because she was so hard to settle.
Apologies for the essay, but I wanted to share some of my experiences. Feel free to join us on the 3 month olds thread - we're not picky about the age of the babies and you'll find plenty of similar problems (along with some improvements).