The OP has clearly written capital S, then capital K, then "ids" in her thread title - which, to most sensible people, would indicate that "S" is an abbreviation for something - in this case "step". Indeed, in her actual post she only writes "stepkids". Furthermore, the way she's written it, indicates that if (and it's unlikely) she were ever to speak it out loud she'd say "ess kids" as opposed to "skid", i.e. so there's no intention of any offence.
I do understand though that she would probably get flamed. Sometimes I can't help but feel there's a certain sort of poster just waiting for a stepmum to put any sort of foot wrong just so they can be pounced upon 
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Personally, I don't find "skid" offensive - though to avoid all possible connection to dirty pants (if that's what some people want to imagine) - I'd be more than happy to use "SKid" - as the OP has done. Though I don't because I'd prefer not to be criticised for something which was never my intention. I can honestly say, hand on heart, that I'd never used the term myself (except as an abbreviation) with any derogatory thoughts whatsoever. I do feel it's very different to a racist term like "Paki" .... you would need to have been living in a cave for a very long time not to realise that most people find that extremely offensive, and it's a term which is (sadly) often more or less spat out with scorn, disgust and aggression in the tone of those who still use it.
The "skid" term is one I have only ever seen written down within specific stepparenting forums (this one, and a couple of other, membership only forums). I have never heard it spoken in real life, would never use it in actual speech (because in real life you tend to refer to your stepchildren by their names so there's no need) and, most importantly, it is NOT, so far as I'm aware said with any implied negative intent .... it's simply a hell of a lot quicker to type than "stepchildren" is. Yes - some posters use "DSC" - but (at the risk of a thunderbolt dropping on me for being such a wicked stepmother) - some of us don't, I'm afraid, actually feel that our stepchildren are that "dear" to us and would therefore feel uncomfortable using that term. Some of us have been actively prevented from establishing a normal healthy relationship with those children, so don't really know them all that well. In other cases, the children themselves refuse to come to our homes - or even see their own parent - so again, "dear" might be inappropriate. Other stepparents have more serious reasons not to feel their stepchildren - at this present moment in time - are dear to them at all. It's wrong, IMO, to try to make all stepparents use an abbreviation that doesn't actually reflect the situation they're actually in. Unfortunately - not all of us have the "dear" blended family we'd ideally want!
Anyway - to protect myself I usually type out "step kid" now - but I'm afraid it does annoy me given I never intended any negative connotation previously in using a shorter abbreviation. Maybe it's how the word "skid" is used within your own family ? ..... it's not something I'd ever use, for example, to any child I was speaking to about ensuring they were careful with personal hygiene.
Besides all that, sorry OP, for having gone off track somewhat. Just annoys me that when someone has the temerity to do something "wrong" on this particular section of the site, it's that which is so often picked up on while the OP's real reason for posting - often when they're clearly in some distress - is totally ignored.
Back to the point ...... I was the mother of a stepchild long before I became a stepparent myself .... just to twist your question slightly. I therefore very naiively (as it turned out) thought I had a pretty good handle on blended families as my ex, his new wife and myself had an honest and respectful relationship in regards to my child - and when I met a man with kids imagined that I "knew" more or less, what it'd be like. I was very wrong. My partner is much closer to his older children than he is to my oldest and I have absolutely no problem with that - I have only ever asked, of any partner, that they treat my child with respect and kindness .... I certainly don't expect the same bond between a parent and child to automatically also apply between a stepparent and their stepchild. What does make me very upset - and often very angry too though - is how my partner sometimes quite often appears to favour his older kids above his/my/our youngest. It's borne of course, out of fear - of loss of contact - and is also a reaction to years of shitstirring by his ex who prefers to "get" at her ex rather than see her own children are happy and confident. Unfortunately though, because of all the crap they've been fed, DP now often feels he has to "prove" that he is a decent dad - and again, because of the (questionable) values they've been brought up with, this often manifests itself in double standards and Disney-Dad syndrome - because his older kids believe (conveniently for them) that normal discipline is "proof" their dad "doesn't care", as is any failure to spend money on them, keep them perpetually entertained and so on.
If you spoke to DP he'd insist he treats all the children the same - as most people would. But the reality is different. It's very hard - and I feel I'm fighting fires on a regular basis to try and smooth things out and ensure that all the children are treated fairly, without causing a row.