This is going to be a long one! Sorry guys! 
I've recently bought my first house with my husband and baby DD, and I've had problems with my neighbour from the start. At first we tried to be very neighbourly with our neighbours next door but they have started to try and become very involved in our lives. They constantly have opinions about how we live our lives and are very open about their opinions which are very judgemental.
The first indecent occurred when i was driving my DD over to my DM's before I went to work. The wife came over to me and informed me that babies "shouldn't be taken out in this weather". When I told her I had to get to work she told me "people like you don't have jobs".
Not sure what this means! My DH and I both work full time and obviously won't be leaving our one year old at home while we are gone. DD was in a very comfy snow suit and so wasn't cold at all, and it was around 8 o'clock so she had already been awake for an hour at least!
She and her husband are constantly curtain twitching when we come home or have visitor and I can often hear them shouting things like "She has the baby this time" and "Now she has dogs with her" when I am going into my house!
Today I was just sat on my sofa playing with my daughter when her face appears pressed against my window!
I waved at her but She didn't seem to notice me, so I opened the door and asked what she was doing. She told me she wanted to know who was in the house. When I said it was just me she started asking if my DH was home, when he was going to be home, who would be looking after DD, etc. At this point I made my excuses and closed the door.
AIBU to be concerned by their behaviour? I'm quite young and find this couple quite intimidating; we are both quite young and this couple are in their 40's - 50's with adult children. We bought this house so we didn't have to deal with landlords being so involved with our lives, and now we have a neighbour doing the same thing. We obviously don't want to alienate them as we live in a terrace house and think it might cause problems further down the line, but this couple seem to be watching our every move. So, mumsnet, what do you think we should do? 