Why did it take 3 months for my boyfriend to be charged with vehicular manslaughter

Why 3 months between the accident and arrest? The process of filing a case and issuing a warrant can take time. If someone is not arrested at the scene there can be a lengthy delay between an incident and arrest.

Here is a summary of the process.

First, the police have to finish their investigation. In a traffic fatality case the police would need to complete their accident report, interview the witnesses, and wait on the blood results from the hospital, inter alia. Once that is complete the police will forward the case to the District Attorney. New cases are sent to the intake division where a prosecutors decides which cases to file and which to reject.

If the State wants to file a felony case they must first present the case to a grand jury. In smaller counties grand juries may not meet but once or twice a month. After the grand jury issues a true bill of indictment then a warrant is issued.

The "other family" does not have the right to press or drop charges. The District Attorney has complete discretion over which cases are, or are not, filed.

Intoxication manslaughter is a second degree felony. The maximum sentence is 20 years in TDC, and up to a $10,000. Here are the elements for IM.

§ 49.08. Intoxication Manslaughter.
(a) A person commits an offense if the person:
(1) operates a motor vehicle in a public place, operates an aircraft, a watercraft, or an amusement ride, or assembles a mobile amusement ride; and
(2) is intoxicated and by reason of that intoxication causes the death of another by accident or mistake.
(b) An offense under this section is a felony of the second degree.

What you need now is not generic AVVO advice. Your boyfriend must hire an attorney immediately. IM is a very serious charge and your boyfriend needs an attorney who can properly litigate the case. Start scheduling consultations with local experienced defense lawyers ASAP. Your boyfriend should not speak with the police about this matter until he talks to an attorney.