I don't think they are horrible at all but a bit strong, after all with them you get a 3rd level spell
before quarter-casters like Arcane Trickster (which gets level 3 spells at 13th level).
I wouldn't allow additional castings of the earlier spells, though. If you want another casting, take it again IMO.
If I follow it with all three as you have them it would be:
- 2 Cantrips
- 2 Firsts (two castings per long rest for each spell)
- 2 Seconds (two castings of one of these per long rest)
- 1 Third
A slightly weaker version would be:
Feat: Magic Adept
Prerequisite: Magic Initiate Feat
You have trained to be better in magic then you already are. You gain access to a 1st and 2nd level from the same spell list of Magic Initiate.
Feat: Magic Practitioner
Prerequisite: Magic Adept feat
Your dabbling in the arts nearly rivals studied casters. You gain access to a another cantrip and 2nd level from the same spell list of Magic Initiate.
You would get 3 cantrips, 2 first, and 2 second level spells. All four would be castable once per long rest.
Combing those with ritual caster would make for quite a spell caster IMO.
As a slight aside, wouldn't "Practitioner" come before "Adept" as I think someone who is adept is usually thought to be better?