Hi, am posting now with the promised thoughts. It is interesting to see what a lot of different perspectives this thread has thrown up.
I think there are two issues - (a) understanding why your DP is adopting this approach (considering her perspective may help you find constructive ways of approaching your differences) and (b) finding ways to help her adopt different parenting strategies that are more effective. Apologies in advance for the long post, but I hope there are some points that may be useful.
Now none of us are in a position to answer (a) - you mention some back history which may be relevant here and no doubt you will be able to ponder whether any of what I say below could be relevant. But I do question whether the "anything for an easy life" "lazy" explanations for the behaviour are accurate. It sounds like your DP actually spends much of her time running around after her DS and she would actually find it easier if she was firmer. You say that she would do anything for him. I therefore wonder whether it might help to look elsewhere for explanations for her behaviour - this might help you address things more effectively with her (although carrying out a big post-mortem investigation of her motives with her would probably just annoy her!)
As I mentioned, I am often perceived by my DH as giving in too much to my DS and I would say the behaviour perceived as "pandering" isn't motivated by a desire for an easy life but rather as follows:
(1) a desire, an overwhelming biological desire, to look after and care for my DS. I never had any experience with children before him. During his babyhood I learnt to respond immediately to his cries, indeed wherever possible to anticipate his needs, and this responsive parenting is generally praised by society as good with a baby. However it can be difficult for the mother of the growing toddler to recognise that the child is growing up and to adapt her strategies (I smiled when I came across the below webpage from Dr Sears). Your DP probably still views her DS as her baby.
www.askdrsears.com/topics/parenting/child-rearing-and-development/fathering/father-worrry-wifes-too-attached
You mention the fact that her DS cries rather than talks to her to ask for things. You clearly have observed them carefully. It took a while for me to observe that this was happening with my own DS. Indeed, I think that I had always throughout his life responded so intuitively to his needs that he assumed that I just always knew what he needed - fine with a baby (where it is food/sleep/cuddles), impossible with a toddler when it is more eccentric things they want, such as "only cut my food with the green knife not the red one" Once I realised this I used a similar strategy to you - "no DS I don't know what you want, can you tell me" and with a bit of repetition this sank in. But I wonder whether this tells you something about the dynamics that are still going on?
In similar vein, a 2 year old who wants to hold a rabbit (using your opening example) is probably genuinely upset about it and she is probably motivated to respond to calm that upset.
This responding as if he is a baby motivation for her parenting style will probably diminish with time as she recognises that he is becoming more independent. A 3 year old is a lot more clearly an individual in his own right. In the meantime providing a role model for an alternative parenting style is probably the most powerful thing you can do. I certainly always watched and adopted strategies from friends. It may not be sinking in now, but when she is ready to make that mental move on she will have a whole host of strategies to draw on, and you indicate you are prepared to give this time.
(2) Secondly there might be something in her background. Does she lack assertiveness? If so it can be tough round kids when one DOES need for their own good to assert boundaries. Some issues in my own background made me scared of conflict, which I felt I had to avoid at all costs. I had spent my whole life practising doing this. It was then stressful and difficult coming up against a demanding toddler as one's instincts are saying "you've got to keep others happy". Indeed something which may seem normal and no problem to you (stating and enforcing some rule) can seem a huge thing - as if one is being really mean and has drawn a really big line in the sand. This aspect requires practice (in the same way as one would do if doing CBT therapy for example) - one practices saying "no", seeing that actually the reaction isn't so bad, then next time it doesn't seem quite so uncomfortable, and so on. I am still surprised when my DC do what I ask!
I don't know whether any of the above resonate. I am sure there are many other possible motivators, these are just the two ones I am aware of in myself, but my main point is that it could well be more complex than "laziness". Some of these motivators cloud one's judgment making it impossible to see that actually a different way would be better, as it just seems so unnatural/uncomfortable.
I don't know HOW to resolve your differences. My bet would be that rather than ultimatums, "slowly slowly catchee monkey" is likely to be your best bet. I think parenting issues are difficult to resolve because each person is motivated by an overwhelming need to do the best by their children and when you passionately believe that your way is right and the other's is not, it is hard to listen to someone telling you that you are doing it wrong and that you have to do something different that feels completely unnatural.
From my perspective, I would say make sure you give her plenty of praise. You say she loves her DS unreservedly. Make sure she knows that you have noticed this and compliment her where you can - all the business literature on people management always talks about praising before offering constructive criticism. Also some people don't react well to being told what to do / sitting down to agree rules. You may find it works better in the long run simply to offer an example and give her time. I know I will defend my corner to the death, but secretly afterwards may admit to myself that maybe the other person had a point, and quietly start to adopt some of their suggestions. Example is the most powerful tool. Wait till she is in a better, more receptive state mentally to have a formal discussion. It sounds like if you try now it will fail.
Finally, your DS is now 8 years old so you have been through the toddler years and come out wiser the other side. Your DP is still learning and to some extent needs learn at her own pace. Recently I was reflecting on how with the first DC it is really an experiment, as one is learning on the job. I am sure that I will parent my second DC very differently and be firmer from the start.