Q1) Извини, что пришлось тащить тебя с собой, не дав даже отдохнуть как следует.
To express the idea of "letting/allowing you (to) do something", you usually put an accusative pronoun. So I wonder why it is missing here. Is it because the preceding clause already has "тебя"?
Q2) Извини, что пришлось тащить тебя с собой, не дав даже отдохнуть как следует.
I have no qualms about the verb "прийтись" per se not always being accompanied by a dative pronoun. You can easily assume that "(мне) пришлось" is omitted here.
But given the presence of the reflexive pronoun "собой = мной", I wonder if it isn't necessary to place some subject marker -- in this instance: "мне" -- before the "собой" in order to make perfectly clear to whom the reflexive "собой" refers?