Thanks for all the responses everyone - it's all giving me food for thought. Please excuse the resulting random stream of consciousness... 
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How do I feel about this? Confused, is the answer. I want to do the right thing but I want to achieve a balance too. I'm trying to give her the benefit of doubt and assume that she is just being cautious but I can't help feeling that it is more than that due to her demonstrating other controlling behaviour.
When we first met, she was swapping and changing their access arrangements frequently, usually so she could go out. DP almost never said no to her, even if it meant having to change our plans. Initially I thought it was just a period of adjustment for everyone and again tried to be accommodating, understanding and reasonable about it. In the end, when DP brought up the subject of our future and us eventually having children together, I said I worried about how the swapping and changing (and moreover his attitude towards her demands, ie. Bending over backwards) would impact on us having a child together. He then became more assertive which I believe she didn't like at first. In the interests of balance though, she has at other times been accommodating of his requests (with the proviso that it will change back if she's not happy with any new arrangements).
To my knowledge she is not in a relationship currently but is dating and I've encouraged DP to be a little flexible over having their DCs for now as I appreciate it can be difficult to date as a single parent. Despite not fully trusting her motives, as far as I know she's not been unpleasant about me and was friendly on the occasion we met. Apparently she did check me out on social media when we first started our relationship and passed comment that I was very petty and seemed nice - I was a little uncomfortable with her passing comments like this even though they were nice comments - I just don't like being judged based on a couple of photos. Again I tried to be understanding about her wanting to check me out, even though this was way before any mention of meeting the DCs.
I know in the past she got cross because he took their DCs on a day trip with his last partner and he hadn't informed her. She has also told him he's not to take the DC to certain places. There are no safety concerns etc.
DP's attitude - this is where I get a bit stuck. I feel for him having to please two women at once but equally I feel like he is too passive and lets her control the situation too much. I do often feel he puts her opinion first, even subconsciously. He is often very understanding of her stance and will say things like 'it's only natural that she wants to check you out on facebook'. He won't entertain the possibility that she's doing it for any ulterior motive. Fair enough, he knows her better than I do although I know how the female mind works better than he does 
. She has never withheld access as far as I know so I'm unsure of the reason for his behaviour. I have put it to him that he still has feelings for her which he strenuously denies. I do feel like he should be handling this better however.
I'm sure he does find it difficult to know what to do for the best. He does consult me but I often feel this is an exercise in gaining my approval for him wanting to please her. I usually do because I want him to be happy and I also want to do what is best by everyone. He has made a couple of comments that made me uncomfortable though - I once said I wasn't in the mood to go into her house and he said something like 'is it because you've no makeup on?'. I pulled him up on that because he was implying there is competition between me and his ex when that's not how I feel at all.
So, I'm still not sure how to handle this for the best or even if I should be doing anything at all. I don't want to put DP in a more difficult situation and I also don't want her to have reason to mistrust me, I want her to feel as ok as possible about this but equally don't want her to think she can intrude into our relationship.