dd wants me to feed her again

[Sunflower100]

Dd is nearly 2 so been self feeding for a while. She is happy to feed herself if we are not in the room and she's not too tired/upset. But if we are in the room she refuses to feed herself and holds out the fork/spoon for me. After nursery (3 days/week)she is so tired that I have got in the habit of sitting with her and feeding her as I can't face a tantrum, but I think this is making it worse.
Clearly us always being out of the room is not an option (and I know it sounds horribly neglectful) so do I give in and just go with feeding her or stand firm and refuse to and let her eat nothing?
I'm keen to broaden her diet as she has recently become quite fussy but I see no way of doing this unless I feed her. And if she doesn't eat at meals she is constantly on the snack scrounge.
Am I being too hard on her? Or not hard enough? Any advice or experience would be helpful.

My dd is still like this at 3! I've made it clear that it is important that I know she can feed herself when I'm not there - but that I am prepared to take turns with her when I am there. Sometimes she just feeds herself - but sometimes we take turns. Sometimes counting the spoon/forkfuls helps.

I didn't just outright refuse as I was eager to get certain foods into her at meal times as otherwise, as you say, there is constant whining for snacks.