This seems like a common issue on this board, and I think you have to accept that it's not only okay, but natural, to love your own kid more than you love your stepkid.  The hard part is how to handle that, and I also think it's okay for stepkids to be told that yes, you and the younger one have a special bond because you are her Dad, just like she has a special bond (I hope) with her own Dad.  So while you won't mistreat her, there will be a natural difference in the two relationships.

It's also okay for you to spend time with your daughter alone without SD10 along. Everything won't be fair and equal, and can't be when one is a bio parent-child bond and the other is a stepparent-stepchild relationship.

This difficulty is helping a 10-year-old understand and accept that. Your wife will have to accept that and help her older daughter understand that, too.

I know it is hard to treat a SKID as affectionately as you treat your own child, but unless there are reasons why this 10 yr old girl has incurred your "deep seated resentment", then it seems a shame that she cannot receive some of the affection that she sees her younger half sister getting.  She may be quite jealous of her - and with good reason it appears - if you shower affection on your bio daughter and she feels excluded.   You say SD10 competes for your affection in a needy way - is it any wonder?  She probably idolises you and feels very much out in the cold from the warmth between you, your wife and your daughter. 

I am not sure why this would be an issue given the age difference between the two children.  You say that you want to be able to "smother your daughter with kisses."  Well that would be normal for a 4 year old but pretty weird for a 10 year old.  The types of attention that will make each happy are worlds apart.  Is there an actual issue with behavior with the 10 year old or is the issue more that you resent the fact that she is even there at all?  These things do not get better on their own.  They only get worse unless something is done.

You may be at a crossroad here where you can determine whether you are going to have a reasonably peaceful future household with a tween/teen girl that you can deal with or one that makes your life miserable.  Teen girls are tough under the very best of circumstances.  You would be wise to take stock of what is going on now and find a way to head things off or you are looking at years of hell ahead of you.  It will be worth the effort if it is at all possible.

Before bd came along, if you did and now you've stopped and she's felt the change its not a surprise that she's fighting for attention? And if you didn't show her the attention you're probably getting the same result, she wonders why and trys to get some. It doesn't sound like bm is helping, as she is trying to force or encourage something you can't do. You need to clearly outline to her how you feel and perhaps she needs to shower her bd with attention while you take separate time with yours? It strikes me that as she has 2 loving and present parents anyway it's not necessary that you act like a bio dad would all the time, particularly with physical displays of affection ,  and this is perfectly explainable to her. Hey, I do understand totally except my stage was set a lot sooner.. when ss (3 at time) first started staying hubby forced us into awkward hugs and kisses goodnight etc, ss was confused, and I got one waft of bm perfume plastered all over his comfort teddy. being heavily pregnant I had to hold back the nausea. I immediately set out my stall after that that I can't and won't be physical with him. Its just a shame for her if you are back tracking on something you used to do? 

You have a different choice to make.  I call bullshit regarding it being impossible to feel for your SD.   No parent trees the same about multiples of their own chimderen but most care about all of their children.  They just do it in different ways.

Take the actions of caring and the feelings will grow.  You do not have to feel for SD the same as you feel for your DD.  Quit being unreasonable with yourself and with your SD.  Just be her SP and be a contributing influence in her life.

Go easy on yourself. You could not have foreseen the future and how your feelings would evolve.

I don't think anyone expects you to feel the same way about your SD as you do your DD. Do you think you should? If you do, release yourself from that bondange and move forward accordingly. Nowhere is it written or required that SD's and SM's love their spouse's kids as their own. Some people don't have any kids and SK's become "their kids" and for some, they say they are  honestly able to treat all kids equally. People are doing what is right FOR THEM and THEIR SITUATIONS. It's not a one size fits all approach. Each "family" is uniquely different in many ways.

You can still be affectionate toward YOUR daughter, she's yours. That's normal. Think of the void she might feel if you don't. I would express myself toward my child exactly as I felt like doing, with no regrets. Nobody would make me feel I shouldn't do that, or that I have to give equal affection to another child.

For goodness sake, we are all doing the best we can and know how to.

Skids what i do with my bios. Even my husband gets that because he knows and has admitted his 3 kids with ex aren’t pleasant and vary as mini me replicas of bio mum and she is a psycho.

i love and care and treat for my kids the best i can, ss is an adult and the eldest sd (adult) and sd14 live together on their own and do whatever bio mum and her current husband tell them to do even if this goes against hubbys feelings or wishes.

when you have skids who are disrespectful and unpleasant, faking niceties is not for me and most people out there. Being civil is all that should be expected.

I feel the same. I'm so sorry for any of us in this boat! I dont show my skids any affection anymore. I felt guilty initially but now I know that you have to be yourself and do what you have to do to get by. The biological parent has to pick up the slack. Good luck with this! You have no reason to feel guilty.