You have experienced cowardly AI that loves to turtle, and would make the Spathi (from Star Control) proud. The easiest way to counter that nonsense is to bring fighters - lots of them. Unfortunately, the OP stated about not getting enough carriers to be a viable option.
Two cruisers and two destroyers... what happened to the starter frigates? Gone? Did you buy the bigger ships, or find them? Did you play the tutorial? If not, do it for your next game! You get some free clunkers - Hammerhead, Wolf, and Condor. Condor is probably the most useful.
Four of your ships vs. eight of them? Yes, do not split up your fleet in that case. In that fight, the enemy did not outnumber you enough for them to surround and gang-up on your fleet.
If your big ships have no means to catch the enemy, your only hope is to outlast the enemy with peak performance/CR advantage, and kill them while they are at 0 CR. Put Hardened Subsystems on everything, even if it hurts. AI loves to turtle way too much, even with more aggressive behaviors, which causes fights to drag on. Also, get Fleet Logistics 3 for maximum CR boost for the whole fleet. (The other levels also feature very nice perks.) It is a boring way to fight, but it is effective. Do not chase enemy ships you have no hope of catching. The enemy AI will happily kite indefinitely. If you must stand off in a deathball of your own, and you have the peak performance advantage, wait until the enemy runs out of CR first, then kill them.
Ultimately, you want a massive fighter swarm to deal with enemy fleets with weaker but numerous ships like these. Get Fleet Doctrine 3 to beef those fighters up.
Get Coordinated Maneuvers 1 and Electronic Warfare 1. You want the minor fleetwide speed and range buffs from the start to have either an advantage at best or parity at worst. Yes, once you fight enemies other than pirates, they will have skills too!