I read to about halfway through:
Firstly, you've said you're generally not a jealous personality but this makes you feel sick so either way, this needs nipping in the bud NOW.
Hopefully you have a good open relationship and you can tell DH it makes you uncomfortable: put it down to the frequency more than anything and ask how he would feel if the shoe was on the other foot?
Secondly, it actually sounds like she's being over helpful in the neighbour department but as others have said, why is she not texting you?
I know my neighbours quite well and as a point of protocol I would NEVER message my male neighbours; it would always be their wives so there is zero misunderstanding.
One of my newer neighbours did something suspect: my DH works for himself, she took his number off his van, got him over on the pretext of maybe ordering CCTV, decided she couldn't afford it but has continued to WhatsApp him.
I saw it, felt immediately uncomfortable and asked him how he would feel if the husbands of the street starting texting me random crap..... he understood ASAP and blocked her.... your DH doesn't need to block her but a simple "I'm not sure but wife's home so drop her a text" and repeat as necessary should get the message across.
For all those going "oh that's so controlling, men & women can be friends"...... get in the bin with ya, that is SO rarely the case.