Weird. To me, tattoos are a very personal thing and not something you should get casually. I cannot tell you how many stories I've heard from those who regretted getting one 'on a whim' or as part of a couple or group. Hopefully, your DH will not cave to SS's obsession. 

"I don't think DH quite understands how unnerving it is to be around someone who is trying so hard to get your husband's exclusive attention."

This ^^^^^

SDiablas whine "We just want our Daaaaaaaaad." "We don't know her and we don't want to know her." 

I feel your pain and have similar problems with SD's acting as mini-wives giving their opinion on everything from if we should sell our house to where we should go on vacation. Super annoying. 

"I don't think DH quite understands how unnerving it is to be around someone who is trying so hard to get your husband's exclusive attention."

I am also chiming on by exclaiming I also felt THAT right there too!  I thought this kind of mini wife dynamic was already strange and unnerving between girls and their Daddyssss, In the scope of my experience with SD31 from the day I met her. seeming a bit on the clingy side to DH. I thought it was odd enough that when she was 13 or so, wearing and borrowing his fave sweater, literally latching onto him for dear life like Velcro to his side when I first entered the picture ( I found and old piic of the three of us that first Thankgiving DH and I started dating depicting that) Also still insisting on sleeping in the same bed with him as a teen girl. It felt like to me that she was acting more like a possessive Girlfriend staking some claim to him and keeping me "taking" her Daddyyyyy and getting in between them. It felt like some kind of controlling tactic like she was sending me some kind of message.. I had thought maybe I  was thinking that was a little beyond my perception of a typical father daughter relationship, because while I got along with my own dad, it was never on that kind of level. BUT pressuring someone to get a tattoo...something permanent that shouldn't be taken lightly is really going above and beyond , really overkill. Im shocked my SD didn't come up with that same scheme, for all know she has and I don't know about it yet. 
I would think it was especially expected from a teen , also a young adult like your SS, to crave some independence from your parents and start carving out YOUR own identity apart from them. NOT carrying on some obsession with coercing them to get matching INK. I agree its kind of creepy like its some symbolism for SS wanting to brand and claim DH as his property, That is exactly how I would take it if I were to find out SD were to ever think of asking for anything like that, 
The root of that matter, which we all know, is that these SKIDS are just lost little souls in this world who don't really have any sense of identity or self esteem to cultivate one that doesn't depend on drama and getting sympathy, and other peoples guilt, namely DH or anyone they can con into rescuing them from themselves 

I think the idea of "branding" that a few people mentioned is the key word. If you choose to have a permanent mark that symbolizes something meaningful that's one thing, but if you try to coerce someone into getting one, it does seem a little like "branding". That's a good word for what I think motivates SS too. He wants a sure and permanent sign that he is connected to his "person". For a while he talked about getting tattooed with his friends. Mind you, throughout middle school and high school he regularly discarded plans with DH to be with his friends, stole from his parents to buy things for his friends, and talked about them as though they were his real family. Very sad. Only now that they've drifted apart, SS sees his dad not just as a parent, but there's this added layer of a disordered type of enmeshment that is being added to the relationship which is unnerving. Try explaining that to friends and neighbors who would probably call me a complete a**hole for feeling weird about some aspects of their "bond".

@LittleTypeAmy - "The root of that matter, which we all know, is that these SKIDS are just lost little souls in this world who don't really have any sense of identity or self esteem to cultivate one that doesn't depend on drama and getting sympathy, and other peoples guilt, namely DH or anyone they can con into rescuing them from themselves."

As MorningMia said, this is right on. And if there was anything I could do to help, I would, and I've tried. But as dh recently admitted, there is not a single thing I could do to make SS like me better, and there is nothing I can do to cure him. DH remembers how he felt about his SM and SD as a teen and he realized that I could lower myself, sacrifice my mental health and give up all of my time and energy, and SS would still resent me. Since a bond isn't possible, I just want DH's cooperation to protect boundaries, so that I don't continue to erode my sense of peace. So far, it seems that DH is holding the line while SS is here. He hasn't made plans with SS for me to cook or anything. It's looking like DH might be finally giving me consideration.

But that doesn't mean I can fully relax. The thing about clothes, LTAmy. I relate to your story about the sweater, and walking between the parents. My SS is obsessed with taking DH's clothes and shoes. This has always been true, but it has been on steroids lately. When DH dropped SS off at college, DH told me that he felt almost like he had to rip his boots out of SS's hands who was pleading and insisting that he keep them. This is after weeks of SS begging for them. These boots, as he told SS, are really expensive and DH has had them for a decade and relies on them for work. He let SS borrow them one day and SS didn't want to give them back. More recently, SS is obsessed with DH's jackets. SS was over just yesterday begging to borrow another jacket which by the way was too small for him and didn't look at all like a young man's jacket (SS is 20 years old! The jacket is made of suede and looks a little honky tonk). But SS insisted on borrowing it and promised to return it the next day. He used to do that with his friends too. I suspect that it was a ploy to force them to see him again. It seems to me that's the reason for all of this borrowing and returning with dh too. You would think that SS would want to be more independent, but I think whatever his disorder is, it curtails his ability to be self-sufficient whether it's with DH or anyone else. 

I don't know whether it would feel different if SS was a girl. I do remember dating a man whose niece had divorced parents. I was over at his family's with my BS, and his mom, sister and his sister's new husband. My BFs niece kept clinging to my BF. I got the feeling that she was like that with her dad and his GFs too. From that, I concluded that the clingingness is one part emotional and one part machiavellian. She was about 11 years old. Every time my BF announced he was going out or doing this and that, she jumped right up saying, "I'll do that with you!" Even the most boring tasks. It felt to me like learned behavior - to always be the go-to companion and to edge anyone else out. We got along fine. I wasn't worried about it since I didn't have to see her al that often. But I did feel sorry for any woman who dared to date her dad!