I agree that what your children do is perfectly normal, and that it is great that their continual arguing and not doing what their told doesn't annoy you (although I would suggest that that is only sometimes true, given that you also say you that going out at weekends is easier that staying in, when their behavior is worse), but it clearly does annoy your DP.
Perhaps it wouldn't annoy him nearly so much and perhaps he would be much more relaxed with regards to their behavior, if he felt that their was some agreed means to control their behavior, some level of discipline, and if there was some equal expectation from you both that house rules for the whole family were more or less adhered to and enforceable.
It is, of course, not just the older children, but the whole family dynamics, including where to progress with your toddler. I see you are now thinking about getting a cot (I do hope that if you and your DP do decide to do that, you and he will also, at least, stop night-feeds ... otherwise I visualise the night time disruptions increasing not decreasing!)
It really is absolutely great that you are already thinking about changes in sleeping and feeding arrangements that would benefit the whole family, and might especially benefit you and your DP as a couple. Well done!
Can I suggest that it might be a good thing to now involve your DP in such decision making ..... to ask him what changes he thinks would be beneficial with regards to co-sleeping and BF; tell him what ideas you have for change; ask him how he thinks the changes could be implemented by you both ; tell him your ideas for implementation.
If there are big gaps between your thinking and his, discuss compromising, look for the middle ground ... neither your way nor his, but the middle (I promise your DD won't die of middle ground) and especially ... very especially ... talk about how you will each support the other through the changes, when things get tough (a sort of parents v toddler, for a change).
Finally (for this one little set of changes) talk about how, when things go a bit awry ... when you cave in and feed her; when he opts out and leaves it to you; when you get irritated with each other ... you will later sit down and remind each other that it was a blip, that you still have a common goal, talk about what you both could have done to minimise the blip, and how you could each support the other through the next blip (because there will be one).
Any help?