He didn't want to get rid of a photo of her that was by your bed? What? 

Being upset when being confronted by something that makes us feel a negative feeling doesn't mean that we shouldn't be confronted by those things. Expressing that you're upset also isn't a necessarily a bad thing, so long as it's not being taken out on your partner.

What I'm saying is that anything related to his XW and kids will likely make him in an off mood because it's likely a sore subject. BUT, being a sore subject isn't a good enough reason to not bring up the topic, nor is it a good reason to take his frustration out on you (and if he does, he needs to apologize for it and take active steps to not do that again in the future).

Additionally, being silent about something that bothers you will kill your relationship. You'll end up resenting him, the place, the ex, the kids - everything. You can't be afraid to talk about these things. Part of dating is finding out if you're compatible, and not sharing things that are bothersome to you prevents you from being able to find out if you're compatible. If your fear is that he'll leave you, then you need to accept that this relationship may not be the right one. If you're fear is abuse from him, then we have something entirely different to talk about and how to get you out safely.

In short, these are going to be rough conversations to have, especially if he has never had to actually work through his divorce. However, him being upset isn't a good enough reason to discuss it. It bothers you. It's not something you want in a relationship. He has to decide if your wants are reasonable to him without taking out his own frustrations on you. He can be upset about it being brought to his attention, and he can feel how he wants to feel. But yelling at you, threatening your relationship, kicking you out - basically, throwing back all his frustration back on you to push you to not address it - isn't okay. If he does any of that, he either needs to apologize and actively work to communicate better and be a better partner by fixing himself or you need to find someone who can recognize that something stings but doesn't make it your fault that you need to fix or accept.

I think that I would take a day and tidy up all the plants in the garden and accidentally knock the bird bath over. Pretend like you had no idea that there were names in it since as you said it is already covered by plants. 

How long were they married? How old are the kids? Honestly, the fact that she uses the family cottage 5 weeks a year would bother me more than the bird bath.  How is that "for the kids"? The kids can go up anytime with their father or their grandparents.  What if you guys are married for 25 years and his wife of 5 years (or whatever) still visits the cottage 5 weeks a year?

Anyway, I guess there is nothing you can do about that.  I'm not one to usually be bothered by pictures or other remembrances from a marriage, but it does seem odd that they have something commemorating their marriage at YOUR family cottage.  Is there anything from your marriage up there? Or is this still "their" place?  To me, the whole package (letting her be up there 5 weeks a year, her pictures around the place, the bird bath) all screams together that he hasn't let go.

If she's going to visiting 5 weeks a year, it should be more like she's visiting YOUR home, whereas now, it appears that you are visiting HER home. All of that together would bother me.

So speak up.

Would ever be in my bedroom or on display except in kids room.  Birdbath gone,  replace by something else 

This cottage sounds like a shrine that is lost in time and needs to be brought up to date. I can't imagine having to share a home with the ex, but then I wouldn't want to even share air space with Meth Mouth.

I am guessing this is a family cottage that your DH has part ownership in.. and that it is shared with others on "his" side of the family.   I have to say that he was pretty darn generous to allow his EX to continue to use the cabin.  Now, perhaps that is just as long as the kids are minors? and perhaps she also had friends in the area and the kids did and were used to spending their summers and breaks there.. and he is trying to perpetuate that for them... but if it is indefinite... past the time when his kids are of age.. that would be a bit uncomfortable for me.

You will have to explain with some context of how the discussion re that picture on the bedside happened.  I mean, did you "attack" him verbally? or in some way that it would be more instinctive for him to be defensive?  Is he a naturally defensive and "push back kind" so basically any request comes with similar response?  Did he see any logic behind the fact that his current partner would not be thrilled to see pictures of him as a couple with his EX?

If he reacted out of line (which it sounds like).. you may have more problems than a bird bath. Why on earth does he feel the need to preserve the cabin as if it were still his "marital vacation home" with his EX.???

I mean, I get not wanting to be surrounded by mementos of his past life.. (stepkids are enough..haha).. but I probably wouldn't be overly concerned about the bird bath.. but might do some moving around so it isn't in a prominent area where I had to see it all the time.. I am assuming that the home is also shared with others in his family.. so you may be limited in some of the changes.. 

The only real issue may be is if this bird bath was made by some beloved family member who has passed on.. and for that reason.. reluctance to part with it may be high.. can it be changed in any way so the names are no longer part of it?

There is nothing normal about this situation.  Starting with your DH wanting to sleep with you while a picture of him and he ex was right there.  Gross.